11. Limits of theories
flowchart TD A0([La teoria più precisa e generale non sempre elimina le idee precedenti]) A0 --> B1([Non esistono teorie in assoluto giuste o sbagliate: contano le scale e gli ordini di grandezza in gioco]) B1 --> B2([Le teorie sono programmi di ricerca: vengono abbandonate solo le idee che non servono più a niente]) B2 --> B3([La relatività ristretta non ha fatto abbandonare completamente la relatività di Galileo]) A0 --> C1([La relatività generale non si applica al mondo microscopico ed alla struttura della materia]) C1 --> C2([Non sappiamo nulla sulla Fisica vicino alla Lunghezza di Planck.]) C2 --> C3([La relatività generale non ha sostituito completamente la relatività ristretta e la gravità newtoniana])
Where physical theories apply
The most precise and general theory does not always eliminate previous ideas
Each theory has its own field of application in which it makes sense to use it. The theory that is most general, and verified accurately by experiments, does not always eliminate the usefulness of earlier theories, in cases where they are a good approximation to the newer, more sophisticated one.
Theories are research programs, only ideas that no longer serve a purpose are abandoned For example, the aether theory, the hypothetical medium of electromagnetic wave propagation, was abandoned altogether when it was realized that space and time are not absolute, and electromagnetic waves propagate in empty space.
There are no absolute right or wrong theories but scales and orders of magnitude count
In general, there are no right and wrong theories, no true or false theories, these are binary hogwash to be left to philosophers and poets. There are only contexts and orders of magnitude in which it makes sense to apply one theoretical model or another, choosing the simpler one to calculate predictions to be confirmed in reality, within the limits of experimental errors and accuracy in accounts.
General relativity does not apply in the microscopic world General relativity is incompatible with modern quantum physics on those length scales, 10-⁷ m to 10-²² m, the force of gravity can be considered practically zero; it is about 10 ⁴⁰ times weaker than the strong subnuclear interaction.
In the microscopic world, for high energies and fundamental interactions between elementary particles (electromagnetism, weak interaction, strong interaction), only special relativity is used. At low energies, Galileo relativity and semiclassical approximations are commonly used.
We know nothing about Physics close to Planck’s length.
Quantum gravity would have relevant effects only near the Planck length, about 10-³⁵ m. But they are lengths and energies that are unthinkable to reach with humanity’s current technology, about 15 orders of magnitude away (energies a million billion times greater than we can reach). And where all our ideas about space, time, matter, energy are probably completely wrong, perhaps even long before we get to explore that world.
There are theoretical hypotheses and mathematical formalisms to unify quanta and gravity (string theory, loop quantum gravity), but since experiments on those length/time/energy scales are impossible, there are no data to confirm either hypothesis with certainty.
General relativity did not replace special relativity and Newtonian gravity
General relativity applies to large-scale phenomena such as those in astrophysics (galaxies, cosmos) for very intense gravitational fields (black holes, massive stars). On smaller scales and for weaker gravitational fields, special relativity with Newton’s law of gravity is sufficient and sufficient.
Narrow relativity did not make Galileo abandon relativity
Similarly, if the velocities involved are small compared to that of light in a vacuum, Galileo’s relativity, with its absolute time, is sufficient and sufficient. That is still used in the most advanced research in atomic physics, structure of matter, solid-state physics, in general in low-energy phenomena.
- Quoted in John Wheeler, Edwin Taylor - “Spacetime Physics,” ch. 3︎