Established Member
We agree that all the underlying laws of the Universe are the same for all the different scales....since 10^-(10^1000) to 10^+(10^1000) meters.
But then...Why we need diferent maths and physics models (for different scales) to explain the same underlying laws of the Universe?
Are these models depend on the scale that is the observer and developer of them?
Why the same underlying laws of the universe behave or are perceived differently at different scales?
Order of Kilopi
Because otherwise it would take years to millenia to do any calculations.Originally Posted by dapifo
Doing a full GR treatment of walking to the store would take pages to write out, and would be completely pointless as the newtonian treatment would be one line and an error of nanometers.
Doing a full QM treatment to find the pressure of a SCUBA tank you would require the processing power of the entire planet for centuries. Again you would find the error from the single line classical statistical treatment to be tiny.
The simplifications make it possible to do calculations and actually make the math comprehensable. As the computing power of humanity has increased, science has been able to get closer to the first principles that underly everything. An example of this is the GPS system. 40 years ago, GPS would have been much less accurate because the computers of the time would not have been able to figure out the full GR treatment needed to get down to sub-meter accuracy.
Established Member
Bingo! A buddy of mine recently introduced me to the investing rule of 72. Take 72, divide that by the interest rate, in percentage, and then you have the number of years it takes to double your money. Meanwhile, I'm trying to guesstimate the answer in my head using the 'real' rules. We both got the same answer, 24 years, but he got it a lit quicker.
Right tool for the right job!
How much gas will it take me to drive 30 miles if my car does 30 mpg? Do we really need quantum mechanics to figure that out?
Order of Kilopi
In a word: abstraction.
Transistor and process designers have to take quantum effects into account.
But you don't have to worry about individual electrons when you design electronic circuits; just voltage, current and the transistor parameters.
You don't (usually) have to worry about those details when you design logic circuits; just 1s and 0s.
You don't have to worry about binary when you program a microprocessor; just the C++ (or whatever) code.
You don't have to worry about the processor architecture or C++ code when you want to watch YouTube.
Trying to model the behaviour of every component in the server, Internet and client when playing a video, using quantum theory would be ... intractable.
Established Member
Are you sure that this (make calculations easyer) is the only reason?
Established Member
Yes
Order of Kilopi
It is a very good reason for taking shortcuts at scales in which we can get away with it.
Established Member
And Why there are not valid the same models for the different scales?
As long I know...till nowdays there are not any model that could explain all the known scales of the observable universe....GR and QM are not yet unified....
Scientifics have needed two different models to explain larger and smaller physics scales.....GR and QM...possibly soon they will be able to unify them...with M-Theory or similar one (since 10^-35 to 10^+27 meters)...but what will happend when the scale range will be extended or amplified?
Do you think that the limits of this scale range will be allways the same?
Order of Kilopi
Why do you keep asking the same question over and over again?
Different scales use different models cause it makes it easier. That will always be true. No one will ever use GR to determine the dynamics of a car on a freeway. Classical theory will always be in use because it describes most of the world with sufficient accuracy.
More detailed theory will be used in more detailed applications. You cannot do GPS without GR. You cant do particle physics without QCD.
The thing is, none of this has anything to do with scale. Microscopic applications will always use QM. Everyday applications will always use classical theory. However, also remember that we dont know everything. QM and GR not mixing is the biggest one, but there are all sorts of places where the actual results of theory arent known simply because no one has ever done the calculations to see what happens.
But when you boil it down, current theory covers all the scales we can see fairly well.
Established Member
Yup, in theory you could use the basics of GR and the Standard Model and work out everything. You might need a second universe, one full of computers, to do the calculations but that basic fact remains true. And when we unify GR and QM then the same will be true of that theory. You could use it to do everything. But under different circumstances different models are more useful. I have no idea why you are so obsessed with scale - as an example I use QM to understand an atom. I use QM to understand 2 atoms. I do not use it to understand a million, I use condensed matter techniques. It is not always about scale, it is about complexity of the system being studied and which methods suit it better.But when you boil it down, current theory covers all the scales we can see fairly well.
Established Member
Rather replace "scales" with "phenomena". We cannot use GR to model atomic phenomena nor can be use QM to work out the orbit of a planet. Neither theories give a complete picture of the universe and both are needed.
Banned
I don't know what your numerical figure is saying exactly off-hand, however, not all physical systems share the same attributes. The idea of explaining laws is by linking them with other laws. Our ultimate goal is to find some unification of the forces. It may be futile to find such a unification however due to it's complexity. It may take us longer than the lifetime of the universe to find out such an understanding.
All systems differ in some way, what we need to do, is find out why they differ, then unify these differences in such a way that only a few people understand it
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