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black magick hustla
17th March 2009, 07:53
Everybody knows einstein's very "particular" way of doing science. While the development of quantum mechanics in the 20th century was the product of probably thousands of scientists, with the theoretical constructs themselves being the conclusions of various really offbeat experimental results (black body radiation, hydrogen spectrum, electron diffraction, etc), einstein's approach to science was very interesting.

We cannot say that QM was the discovery of only a man, but we can almost certainly say that general relativity, atleast as a theoretical framework, was the work of only Einstein. even the 60s and 70s cosmologists have apported very little to the theory itself. For example, I read an amazon review accusing a lot of the "general relativists" today giving off this vibe of "revolutionary scientists" by publishing lots of gimmicky pop books about time travel, black holes etc, while in reality, they have done very little after einstein.

What boggles my mind is the "philosophical" implcations of einstein's work. this man's science was almost entirely based on thought experiments. not only that, but it is completely counter-intuitive. I generally treat his gravitational theory of curved-spacetimes as a mathematical model, and in that sense it might make more "sense". However, the geometrical assumptions that led einstein to treat "space-time" like this is really mind boggling. Even if quantum mechanics is really weird, the most sober QM theorists never assumed something beyond the fact that there was a wavefunction that happened to give an estimation of the position of the particle. I.e. QM was based on those observations. General Relativity was the product of a man sitting in his office, assuming there was something like a "space-time manifold" and then treating it as malleable by the energy in the universe.

now, we might relegate GR as just a mathematical tool, like most physicists have relegated the wavefunction as simply an "information wave" i.e. not a real wave like a sound wave or an EM wave but just a mathematical wave. However, there is something called a "gravitational wave" that can be "pictured" as ripples in spacetime, if we treat spacetime as some sort of giant ocean. It is assumed this exist because of the behavior of things like pulsars, which seem to to loose energy through some sort of unknown radiation. G-waves have not been detected, but there are some detectors spread around the world and it is assumed they exist.

If gravitational waves are detected, then it means that space-time is not just some mathematical gimmick, but a real entitiy. It would have the same effect as the discoverey of E-M waves by maxwell, which relegated magnetic and electric fields from some sort of mathematical tool to a real entitiy that propagates in space.

my point is, if mathematics are just mental constructs or a language, how is it that a man that sat on his ass scribbling numbers all day was able to come up with a model of the universe which has a surprisingly predictive power and is completely counter-intuitive. For example, for all the mathematical sophistication of classical mechanics, the mathematics it uses, like the differential equation, is completely intuitive once you have a grasp of it. For example, by simply looking at the behavior of something, even me, some undergrad physics rookie, can come up with a differential equation for it simply because the difeq is very intuitive, kindof like using language to express something. However, the math of GR relies on a sophistication beyond intuition and worse, it was the product of very little observation compared to other "counter-intuitive" theories like QM. newtons mechanics might have been mostly the work of only one man, but they were based on very elegant intuition and on very empirical assumptions.How does a sober materialist deals with this?

Dooga Aetrus Blackrazor
17th March 2009, 08:40
One way of considering this problem is convention. You could argue that had you been raised with the views we now know, you would think them as intuitive as Newtonian views. As our conceptions, society will have to evolve with it. That process will be limited by how fast people can begin to comprehend the views. Right now the academic community doesn't have a consensus on how to understand many of these issues.

http://en.wikipedia.org/wiki/Four_dimensionalism

That can be seen as a consequence of modern physics. With respect to identity through time, Mark Heller has a compelling view. Objects are four dimensional hunks of matter that move through spacetime. I've reached a level of semi-understanding, but I'm not sure I can fully understand it. I have an essay I wrote on the topic with respect to the Ship of Theseus problem, and I can post it if you're really interested.

Plagueround
17th March 2009, 08:43
I actually followed this much better than I used to be able to, but I'll be damned if I can formulate a reply. Time to hit the books again. :bored:

Rosa Lichtenstein
17th March 2009, 10:30
Dooga is on the right lines here.

Consider an analogy: in linear programming we can use as many as ten million variables, each representing a dimension along a defined axis.

So, in elementary algebra, we use two or three variables. When you were 13/14 you might have had to solve these simple equations:

1) 2x + y = 0

2) x - y = 3

algebraically or graphically.

In order to represent this solution, you would have to draw two orthogonal axes (i.e., at right angles), an x and a y axis, and then intersecting lines that these equations express, etc.

In order to represent three equations, say, in 3 unknowns, you need to add a z axis, and draw intersecting or non-intersecting planes.

When this method is used in, say, economics, no one imagines that these representations depict anything in the real world, even though they provide real solutions and can be used to make accurate predictions.

So, if an economic problem (or one in discrete mathematics) requires, say, 10,000 variables, and even though we cannot physically represent the complex space that woud be required to draw the manifolds that the relevant equations could be used to depict, we can still use computer software to find a solution (if there is one). But no one imagines there is a 10,000 dimensional space, with 10,000 orthogonal axes 'out there' somewhere that this impossible to draw picture represents. And yet, these models can provide precise solutions and make accurate predictions.

Same with the complex spaces required to solve equations in relativity and QM.

Of course, anyone who thinks otherwise will have serious problems explaining how such things as time lines, geodesics, differential equations and tensors can actually make anything happen or move.

Worse still, they will find it impossible to explain what these mathematical objects represent in the physical world.

Does anyone, therefore, imagine that there are infinitely thin, invisible, super-strong, permeable curves running through all of space-time (which objects can easily pass through as they move) that are the correlates of geodesics, or that there are real numbers floating about in space that are the correlates of scalar fields?

If so, they will have no problem believing in the Tooth Fairy and Big Foot...

In short, modern physics has absolutely no philosophical implications whatsoever.

black magick hustla
17th March 2009, 20:42
That is more or less what I think is. The issue here Rosa, has more to do with einstein's approach to science. As I said, if gravitational waves are discovered, then curved spacetime is "real", in the same way electric fields and magnetic fields are "real".


What is interesting though, is that ultimately einstein was unable to accept QM in its totality because of his strange approach to physics. While experimentalists had very few problems accepting QM, Einstein did, because his way of science was creating this beautiful geometric models of the universe, while the QM approach was less aesthetically pleasing. Perhaps my unwillingness to find your answer satisfactory has more to do with the fact that I am awe-stricken by the idea of a man scribbling numbers and then hypothesizing that light would be curved by big masses, without this man ever having seen curved light. Or the fact that a theologist was able to "predict" mathematically the big bang after finding a particular solution to einsteins field equations.

black magick hustla
17th March 2009, 20:51
Furthermore, I have no "problem" visualizing many variables, its just mathematical formalism. you dont visualize them, you can have four variables that are (x,y,z,T) where T is temperature. Its a mathematical model.

Rosa Lichtenstein
17th March 2009, 20:53
Marmot:


That is more or less what I think is. The issue here Rosa, has more to do with einstein's approach to science. As I said, if gravitational waves are discovered, then curved spacetime is "real", in the same way electric fields and magnetic fields are "real".

The problem with this is that even if these waves are discovered, and the chances of that happening get smaller with each passing year, their 'real existence' depends on the reification of some pretty abstruse mathematics, which would make this move susceptible to the points I advanced above.


What is interesting though, is that ultimately einstein was unable to accept QM in its totality because of his strange approach to physics. While experimentalists had very few problems accepting QM, Einstein did, because his way of science was creating this beautiful geometric models of the universe, while the QM approach was less aesthetically pleasing. Perhaps my unwillingness to find your answer satisfactory has more to do with the fact that I am awe-stricken by the idea of a man scribbling numbers and then hypothesizing that light would be curved by big masses, without this man ever having seen curved light. Or the fact that a theologist was able to "predict" mathematically the big bang after finding a particular solution to einsteins field equations.

My understanding is that he thought QM was incomplete.

Rosa Lichtenstein
17th March 2009, 20:58
Marmot:


Furthermore, I have no "problem" visualizing many variables, its just mathematical formalism. you dont visualize them, you can have four variables that are (x,y,z,T) where T is temperature. Its a mathematical model.

It's not a question of visulaising, here. After all, Escher was able to draw many impossible objects:

http://www.santarosa.edu/~mmcginni/myart/invention/superplexus/escher/RelativityESCHER-410px.jpg

http://robertarood.files.wordpress.com/2008/09/escher_ascending.jpg

But whether is necessary to postulate real dimensions corresponding to mathematical objects (which dimensions are also susceptible to the points I made earlier).

black magick hustla
17th March 2009, 20:59
:shrugs: But his concept of "incompleteness" sounds like a rejection to me. The most important aspect of QM is uncertainty and that it is intrinsic to the nature of experiments that certainty is unfeasable. to reject this is to reject QM as an approach to science. He thought it was incomplete probably because his way of doing science was first doing the math and then looking for results, not the other way around.

Rosa Lichtenstein
17th March 2009, 21:09
Marmot:


But his concept of "incompleteness" sounds like a rejection to me. The most important aspect of QM is uncertainty and that it is intrinsic to the nature of experiments that certainty is unfeasable. to reject this is to reject QM as an approach to science. He thought it was incomplete probably because his way of doing science was first doing the math and then looking for results, not the other way around.

He thought it incomplete because he could not accept the Bohr-Heisenberg model (which seemed to make quatum reality dependent on human observation, and clearly indicated that nature was not deterministic).

Now, wherever the truth lies, the history of science has taught us that the vast majority (if not all) theories end up being rejected parially or wholly.

In that case, only a very naive philosopher will pin his/her ideas on what scientists tell us about nature.

But, as a Wittgensteinian, I would argue that even if scientists never changed their minds, what they have to say is of no philosophical relevance.

Why that is so is rather involved, and if I can summon up the energy, I will try to say (here) why that is so (in less than 1000 words!) one day.

Anyway, I will be publishing a long Essay on this in 2010.