# Will a GUT or TOE be mathematical

## Main Question or Discussion Point

Most if not all laws of physics are not mathematical, rather statements that define the way mathematical models must follow. They have been laid down by intuition and observation.
So how can something like string theory based on maths be expected to achieve a GUT or TOE if it does not know whether or not it is following the correct rules.
A theory of everything must describe the start of the universe not necessarily mathematically but by laying down the conditions that led to that beginning from which the maths will emerge.

Related Other Physics Topics News on Phys.org
Drakkith
Staff Emeritus
I think you have a misunderstanding. A scientific law is only one piece of a larger Scientific Theory that combines multiple laws together and forms a model that is the end product of the theory. At their heart, ALL theories are mathematical theories, as without math there is no way to explain or predict anything. A GUT or TOE that describes the initial conditions that led to the beginning of our universe MUST be based on math.

Pengwuino
Gold Member
Most if not all laws of physics are not mathematical, rather statements that define the way mathematical models must follow. They have been laid down by intuition and observation.
So how can something like string theory based on maths be expected to achieve a GUT or TOE if it does not know whether or not it is following the correct rules.
A theory of everything must describe the start of the universe not necessarily mathematically but by laying down the conditions that led to that beginning from which the maths will emerge.
What?! EVERY law of physics is mathematical.

cepheid
Staff Emeritus
Gold Member
Most if not all laws of physics are not mathematical
This is patently false.

What?! EVERY law of physics is mathematical.
Seconded.

Example of a physical law: Newton's second law of motion: "The net force on an object is equal to its mass times its acceleration."

The net force on an object is equal to its mass times its acceleration is a statement of fact that the maths has to follow, maths is about numbers the statement (law) has no numbers in it but describes the way the numbers must work. 2+2=4 means nothing on its own but with a description of what it relates to i.e 2 apples + 2 apples = 4 apples it has meaning.
Or I give you 2+2 = the creation of the universe all that gives you is 2+2 what? The numbers have to relate to something you cannot know what that something is through pure maths.

Pengwuino
Gold Member
The net force on an object is equal to its mass times its acceleration is a statement of fact that the maths has to follow, maths is about numbers the statement (law) has no numbers in it but describes the way the numbers must work. 2+2=4 means nothing on its own but with a description of what it relates to i.e 2 apples + 2 apples = 4 apples it has meaning.
Or I give you 2+2 = the creation of the universe all that gives you is 2+2 what? The numbers have to relate to something you cannot know what that something is through pure maths.
"mass times its acceleration" - that is a mathematical statement. A non-mathematical description of Newton's 2nd law would be "Given a force, there exists a relationship between the object's mass and its acceleration". That's non-mathematical. That also tells you nothing and is not physics in of itself.

The net force on an object is equal to its mass times its acceleration is a statement of fact that the maths has to follow, maths is about numbers the statement (law) has no numbers in it but describes the way the numbers must work. 2+2=4 means nothing on its own but with a description of what it relates to i.e 2 apples + 2 apples = 4 apples it has meaning.
Or I give you 2+2 = the creation of the universe all that gives you is 2+2 what? The numbers have to relate to something you cannot know what that something is through pure maths.
The vast majority of physcisists will disagree with you. Newton' second law relates measurable quantities (mass, acceleration, force) in a precise way that allows one to use symbolic manipulations and/or geometric reasoning to derive new statements of fact that are not obvious from the starting assumptions. It is a uniquely mathematical approach to understanding the physical world. For example, Kepler discovered his three laws of planetary motion without really understanding why they were true. Newton was able to show that his second law of motion together with the law universal gravitation were enough to derive all three of Kepler's laws. The reasoning that Newton used in the derivation was geometrical. It is more common nowadays to use algebraic/symbolic manipulation to arrive at the same result. Regardless of the methods used, all understanding in physics ultimately derives from mathematical reasoning.

On further thought I think the origional question should have been
Will the final theory be found through purely mathematical means?
Appologies.

Drakkith
Staff Emeritus
On further thought I think the origional question should have been
Will the final theory be found through purely mathematical means?
Appologies.
If you mean without any observations then I'd say that's very unlikely.