What Are the Fundamental Assumptions of Modern Physics?

[fractalzen]

It seems to me that classically physics is based upon the idea of measurement, that the length of a meter, the duration of a second, and the mass of an object is the same for one person as it is for another. Wheeler in his Geometrodynamics further was able to express mass and time in terms of length. So if we use Wheeler we can say that the basic assumption of classical physics is that the meter is the same length for me as it is for you. Classical physics assumes that in the "real" world things have fixed length, and don't constantly change lengths as might be possible in a dream.

So along comes relativity and quantum mechanics, and now the length of meter is no longer the same for everybody, but varies according to relative velocity or its position in a gravitational field or its quantum pdf.

Okay so now what? What is the basic assumption of "modern" physics? It seems to me that energy is a more fundamental concept than length, but isn't energy defined in terms of length, mass, and time? So is modern physics still using the "my meter is the same distance as your meter" assumption? If not, what has replaced it?

**/ The idea that everything that I am aware of in the vast universe around us is taking place inside my, by comparison, infinitesimal brain, indicates that perhaps size and distance might be viewed as constantly varying qualities rather than fixed quantities. **/

 

[mfb]

What is the basic assumption of "modern" physics?

Something like this:
There are inertial observers. The speed of light (measured as in classical physics) is constant for all inertial observers. (special relativity)
Quantum mechanics
Gravitational acceleration does not change physics locally, energy density bends spacetime. (general relativity)

but isn't energy defined in terms of length, mass, and time?

In the SI unit system. But this is completely arbitrary. You could use energy as fundamental unit, and express length as $1m=1s\sqrt{\frac{J}{kg}}$. In particle physics, it is common to express mass, momentum and (sometimes) time and length in terms of energy.

 

[DennisN]

I'm not sure what you are asking, there is no clear fundamental definition of energy. Energy comes in many various forms and can loosely be described as the capacity to perform work.

As an example, the energy of a massive particle at rest is E=m_oc², which is basically the mass multiplied by a constant; the units are obviously in terms of kg,m,s but the constant is c² m²/s².

Futher there are many other "assumptions" of modern physics like (intrinsic) electric charge, spin (intrinsic angular momentum) and a bunch of other physical constants. The masses of all particles are also "assumptions" in the sense that they do not automatically "pop out" (yet) from a deeper underlying theory.

"...perhaps size and distance might be viewed as constantly varying qualities rather than fixed quantities."

In what respect would they vary and why would you think so? Are you experiencing that your height is constantly varying?

(I saw mfb had already replied about relativity)

 

[Crazymechanic]

Well in strong gravity height can indeed vary as mass is "squeezing" particles more tightly together and the size they took up here on Earth would not be the same on some other much larger planet or object.