Is physics possible without spacetime dimensions? One of the most central concepts in physics is energy. But on a deeper level energy is the same thing as information. Classically information about a system is given by spacetime coordinates and their derivatives. How much physics can be done without ever referring to time and space directly, calculating the physical properties like temperature, charge, etc?
 A: There are seven fundamental SI units:


*

*meter

*kilogram

*second

*ampere

*kelvin

*mole

*candela


Excluding space & time would mean excluding meters and seconds. If you look through the list of derived units to see which do not involve meters and seconds, there're very few units that do not. These are:


*

*Celsius. This is trivial, of course, since it's just a change of units.

*Angular units (radian, steradian). This wouldn't mean anything without space.

*The unit of exposure (coulombs per kilogram), which measures the amount of exposure to x-rays and gamma rays. This does sound like it doesn't depend on space & time, but it's surprising because x-rays and gamma rays are not directly related to coulombs. It turns out that if you look at the Wikipedia article's on radiation exposure, it's actually measured by "the electric charge freed by such radiation in a specified volume of air divided by the mass of that air". Volume, i.e. space, is necessarily involved.


Therefore I conclude that there are very few equations you can write that do not involve space or time, and by extension physics is not possible without space & time.
A: We can't accurately describe the world around us without describing the spatial dimensions as we interpret them. Your question borders on the edge of philosophy, as it brings up the question of "how do we define 'physics'?" All I can speak for is human interpretation of the universe we are in. Maybe it is possible for information to exist in an n-dimensional space that we are incapable of interpreting, but if that were the case, it would be counter-productive for us to try and accurately describe it as it lies beyond human comprehension.
A simple definition of physics could be the study of matter and its properties. If you don't study an object's size and shape, you wouldn't have a full description of its properties.
A: In classical and quantum mechanics, you are normally interested in how physical observables evolve in time e.g how a force changes its value in time $F(t)$ in classical mechanics or how states evolve in time $\vert \psi(t)\rangle$ in quantum mechanics for example.
There are some theories aimed to describe certain phenomena that do not involve continium space variables at all. For example in the Ising model, in wich you want to study the properties of a bunch spin-interacting particles.
$H(\sigma) = -\displaystyle\sum_{\langle i~j\rangle} J_{ij} \sigma_i \sigma_j - \mu \sum_j h_j \sigma_j$
Even though you need some sort of time variable to get dynamics. However, even if u don't need continium space variables to explain the physics, it doesn't mean space isn't there. 
Your question also reminded me to background independent approaches to quantum gravity, such as Loop Quantum Gravity, since a theory that aims to explain the origin of sapce-time itself should not depend on space-time variables. Hope this helps, cheers!
A: Much of the core structure of thermodynamics can be derived without reference to space or tie --- or to be more precise, one needs to refer to processes that transform physical systems from some initial state to some final state, but without necessarily referencing any concrete time units.  For examples, see:


*

*Lieb and Yngvason, "The physics and mathematics of the second law of thermodynamics", Physics Reports, 1999 --- derived the structure of the entropy function from axiomatic reasoning, see also https://en.wikipedia.org/wiki/Adiabatic_accessibility.

*Sparaciari et al., "A Resource Theory for Work and Heat", Physical Review A, 2017.

*Bera et al., "Thermodynamics as a Consequence of Information Conservation", Quantum, 2019.
