Can physics be done without the use of time? Carlo Rovelli is interviewed in this article (The illusion of time):

Alongside and inspired by his work in quantum gravity, Rovelli puts forward the idea of 'physics without time' This stems from the fact that some equations of quantum gravity (such as the Wheeler–DeWitt equation, which assigns quantum states to the Universe) can be written without any reference to time at all.

From Wikipedia:

In theoretical physics, the problem of time is a conceptual conflict between general relativity and quantum mechanics in that quantum mechanics regards the flow of time as universal and absolute, whereas general relativity regards the flow of time as malleable and relative.

In this article (Quanta Magazine, by Natalie Wolchover; Does time really flow?) the issue is further discussed.
I'm not sure I understand doing physics without time. Why does it stem from a conflict between GR and QM? Let it be clear that I'm not referring to block time.
I have little understanding of the Wheeler-deWitt equation.
So the question is: Can physics really be done without using time? It seems impossible to me. GR and QM may be putting forth different notions of time (absolute vs. relative), but nevertheless.
The difference between time used in GR and QM (I do know that the Wheeler-DeWitt-equation tries to reconcile the two: the equation is trying to unite GR with QM) doesn't mean that time is superfuous.
I know this sounds all quite philosophical, but I have brought in the physics.
 A: Rovelli's The Order of Time is an excellent book and well worth reading if you haven't already. I don't think Rovelli is advocating doing physics without time (the article adds spice by exaggerating his position somewhat). Instead, he is suggesting that time is an emergent phenomenon rather than one of the fundamental attributes of reality. But it is a useful shorthand, and trying to do physics without making any use of that shorthand would be at best tedious and at worst incomprehensible.
In a similar way, we know that colour (in its everyday sense) is an emergent phenomenon and not an attribute of fundamental particles. However, we still talk about "redshift", for example, as a useful shorthand for "photons with longer wavelengths and lower energy", and describing a van Gogh painting without referring to its colours would be a pointless and uninformative exercise.
The question of whether time is fundamental to reality or an emergent phenomenon is not settled - which is what makes it so interesting. Julian Barbour's The End of Time presents a more extreme and definitely less mainstream view than Rovelli's. On the other hand, Lee Smolin's Time Reborn puts the opposite case and argues that time really is fundamental.
A: Since this discussion is, by the author's own admission, delving into the theoretical and philosophical, I believe it is just as important to answer the question practically.
Even looking into the nature of the word physics, one would find that it has a Greek origin and meaning: nature. The coining of the word physics itself is intended to convey fundamental, source-like practicality to science. Physics should, therefore, be rooted in the scientific nature of the cosmos, another ancient Greek word and concept.
Beginning with a negative proof of time as a fundamental part of nature, I take you to the kindergarten classroom. Here, in our fundamental learning facility, we observe children who need guidance and nurturing. Our first pupil comes in from "recess," a time in which the child existed in the cosmos as a wanton, carefree denizen of the "playground," which for all intents and purposes here is a place in which the pupil encounters a dirty environment. Our first pupil's skin has surface contamination, and so the instructor demands that the pupil go immediately to the washroom and clean off the dirt from his skin.
Here is where time gets really important. The first pupil, heretofore referred to as P1, as if motivated by some unnecessary wantonness, returns from the washroom in literally no time. P1 spends 0 days, 0 minutes, 0 seconds inside the washroom, declares the cleansing complete and attempts to return to the classroom. Even a rudimentary knowledge of physics would determine that P1 is in gross error. However, that is not sufficient proof. Because even if the pupil has spent 20 minutes inside the washroom, the instructor will not permit re-entry to the classroom without evidence of a physical and/or chemical process that could have cleaned P1's skin.
We can continue this proof to point at which we arrive at a practical solution, to wit, P1's skin is clean. It will become increasingly obvious in such a situation that P1 is generally supposed to use running water, vigorous motions of the body, and a chemical solvent to perform the cleansing. While there are numerous options by which to choose from, the kindergarten teacher will often need to explain and teach the child to process the skin with an aqueous chemical solvent, surfactant, vigorous motion, and a very practical element which cannot be "found" inside the washroom: time.
Because a lot of pupils believe that washing the skin is complete immediately upon contact with the soap or water. P1, and perhaps some physicists, need to understand that there is a chemical and physical process that takes place while standing at the sink, and time is a critical element in this ... and every ... physical, (Greek: natural) process.
How many physicists have not learned this simple truth about physics itself? If there is no time, then there is no process. And with no process, there is no action. And with no action, there is no practice. Impractical physics, that is, physics with no time, is not natural. If you remove time from physics, or you disallow it or ignore it, then you must be talking about the supernatural. And that is the full circle of practical physics colliding with philosophy. A philosophical physics, sans time, is one and the same as a physics with no truths and no parameters: it is timeless, without bounds, unnatural, metaphysical, and as Pupil P1 showed us: absurd, illogical, impossible, erroneous, naive, and ignorant. It might even be a bit of a dirty trick.
The only physics possible without the element of time is one outside of this cosmos that was created with it. If you leave out time, physics devolves into one of two things: the endless paradise of God, or the bottomless pit of Hell.
