Monday, March 1, 2010

Are Physical Theories Just Models?

Look at the figure to the right.  There is a physical world which we observe.  From these observations we derive physical laws.  (Usually expressed in mathematical statements).  A question arises: Is the universe really obeying these laws or did we just get lucky in finding something that models the behavior we observe? 

Moreover, can we ever know?

Here is a similar thought by Peter Szekeres:
When we consider the significant achievements of mathematical physics, one can not help but wonder why the workings of the universe are expressible at all by rigid mathematical 'laws'. Furthermore, how is it that purely human constructs refined over centuries of thought, have any relevance at all?... Some of these questions and challenges may be fundamentally unanswerable, but the fact remains that mathematics seems to be the correct path to understanding the physical world.
Though the above is philosophical, I think it is still worth pondering. 

To Me It's Okay Because The Models Have Predictive Power.

Even if physical theories are no more than models, I still find the pursuit of science very valuable because of its predictive power.  Models or not, modern scientific theories predict masses, velocities, positions, charges...  From these predictions we can create electronics, build cities, cure diseases, etc...

Science therefore does not suffer from the same thing that plagues many other philosophical constructs. For example, from Steven Weinberg:
Why was Aristotle... satisfied with a theory of motion that did not provide any way of predicting where a projectile or other falling body would be at any moment during its flight...? According to Aristotle, substances tend to move to their natural positions... but Aristotle did not try to say how fast a bit of earth drops downward or a spark flies upward. I am not asking why Aristotle had not discovered Newton's laws... 
What puzzles me is why Aristotle expressed no dissatisfaction that he had not learned how to calculate the positions of projectiles at each moment along their paths. He did not seem to realize that this was a problem that anyone ought to solve. 
Even if physical theories are only models of reality, with modern science we have real predictive power so Aristotle's problem no longer exists and I believe this is a wonderful thing.


  1. I think to truly understand science is to truly grasp this predictive power! At times incredibly precise, like predicting the CRB, and other times vague yet so profound, like Darwin predicting some biological mechanism for passing on traits allowing for random modification. I don't know why people get all excited about psychics and Nostradamis when science gives us so many precise and verifiable predictions every day. And every once in a while science gives us a cool gadget to put in our pockets!

  2. Well said Stan "To truly understand science is to truly grasp this predictive power!"

    What a great quote which should really underscore why science is so special.

    Just because you have a cool sounding theory that makes logical sense doesn't mean it's helpful. (Example: Aristotle above.

  3. To be fair though once people worked out Aristotle more it had predictive power. This is why the actual Copernican revolution was much more complex than it first appears. (Something Kuhn in particular makes hay with) At the time both the Copernican and Ptolemy models predicted with fair accuracy where the celestial objects were.

    Now Newtonian physics was a breakthrough, of course. But I'd argue the real predictive breakthrough was the practical application of calculus to mechanics. But honestly that was much more due to Leibniz than Newton. I don't know if you've tried to work through the more geometric approach of Newton. It's pretty difficult and I confess I didn't get too far. (More due to time than anything) But I think it was Leibniz to whom we really owe a lot of credit. It was that practical ability to mathematically make predictions that revolutionized science. Of course a strong case can be made that Leibniz plagerized the calculus or at least discovered his form after Newton. But there's a reason why we followed the Leibnizian trajectory (pardon the pun) of mechanics.

  4. It is true Aristotle's contribution should not be underrated as his ideas did lead to major intellectual revolutions, like the "Copernican" one you mention.

    Also, you're right Leibniz's contribution to calculus is amazing.

    And who could have come up with a better notation than dy/dx? Seriously, Leibniz's notation alone has made calculus incredible intuitive and doable.

  5. "the more geometric approach of Newton." Yeah, I'm always fascinated that people could actually read Newton's Principia as well as they did back in the day.

    Even with years of formal mathematical training in calculus, which they didn't have, Newton's book is still hard to piece through.

  6. It is true that the work of Aristotle had to be improved, and even if we need a new model for gravity, it is true that the mathematical work for prediction of Newton will remain ; this is how sciences are done currently, there is a lot of contributions going together : science is then a work of collaboration.

  7. Cartesian, your right, science is a work of collaboration. Even Newton admitted to accomplish his own work that he stood on the shoulders of giants.

  8. One of my favorite quotes is "All models are wrong. Some are useful." Whether or not this quote is accurate, I think it underscores what you're trying to say about science. It's power comes in its utility. It can predict things and "every once in a while science gives us a cool gadget to put in our pockets!" I think it can be missing the point a bit to argue whether the universe is really obeying the laws we derive or if we are just coming up with better and better models for how the universe acts. Either way, it works.

  9. Bill, great quote.

    Your right, at the end of the day science works!

  10. Joe,

    I used to subscribe to the "it's just a model" way of thinking. Read "The Fabric of Reality" (if you haven't already) or "Myth of the Framework" to get the other way of thinking (and in my view, the more correct.)

    These aren't just models, they are explanations. As the "model" gets refined to be more accurate, the explanation is therefore provably closer to whatever the truth is. Therefore, science isn't just models for prediction (though it is that too). It's a bonefide study of what reality is via explanation.

    "And who could have come up with a better notation than dy/dx? Seriously, Leibniz's notation alone has made calculus incredible intuitive and doable."

    Intuitive? Hello! You physicists are a whole other species! ;)

    Bruce Nielson

  11. Bruce,

    I have not read these two books but should. These explanations do get better and better and yes, one would hope therefore closer and closer to what the truth is.

    Thanks for your comment.


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