∆The problem of time, wheeler Dewitt and Hamiltonian constraint.

“The problem of time”, “wheeler Dewitt equation” and the “Hamiltonian constraint”.

 

Wikipedia describes the Wheeler-DeWitt equation as...


The Wheeler–DeWitt equation[1] is an attempt to mathematically meld the ideas of quantum mechanics and general relativity, a step toward a theory of quantum gravity. Interestingly, in this approach, time plays no role in the equation, leading to the problem of time.[2] More specifically, the equation describes the quantum version of the Hamiltonian constraint

 (My italics)


It is interesting to note that some interpretations of the Wheeler-Dewitt equation suggest there is no time, and thus the universe may be static.

I think this is the result of wrongly assuming time exists, then in seeing that it does not, taking this to mean 'things cant move'. E.g formulating the instance that 'things take time to move' and concluding thus 'if there is no time things cant move'. Instead of considering "we may have been wrong to even assume things take time to move... there may be no time, and thus things may just move" (as is actually, and directly observed by everyone).

(logically this may be similar to concluding "If we can't find any evidence that yeti's exist, then they must have all killed each other").


The Wheeler-Dewitt entry above states “. Interestingly, in this approach, time plays no role in the equation,”

Implying that ‘time’ might be expected to exist, and might be expected to play a part in the equation.

 However, if we consider any ordinary ‘time based’ experiment, e.g. accessing the dynamics of a stone falling from a tower, we invariably find that anyone conducting the experiment drops a stone, and compares the stones motion to the motion of a steadily rotating hand on a numbered dial (or some other variant).

They will also typically refer to the position of the hand with symbol ‘t’ and refer to it as ‘time’.

While is is extremely useful and logical to compare complex motion to an example of simple regular motion, the fact that a hand has been designed an manufactured to move steadily forwards, and forwards only , does not count as a proof that there is an extra ‘thing’ in the universe that also constantly moves steadily forwards.

Unless proven otherwise this is only an assumption, and while IF there is time, THEN a clock shows its passing, BUT, just  making a machine that displays motion, and calling it a clock in no way proves the existence of time.

(e.g. ‘Calling’ a machine a yeti trap in no way proves yetis exist, (that's enough yetis for one page)).

Thus it may just be that matter can exist move and change, and that we can usefully compare examples of motion, but, equations such as

 D=1/2 g t^2

Might be more genuinely expressed as

D=1/2g H^2

 Where H is the position of the genuine and existing mechanical hand in units of degrees or cm from its origin. Thus the statement “ Interestingly, in this approach, time plays no role in the equation,” – might be rephrased as “we may be wrong to even assume time with a direction exists, thus there is no expectation for it to be included in the equation other than as a value understood to be nothing more than a useful tool”.

 


Re The Wheeler–DeWitt equation[1] .Wikipedia continues

...More specifically, the equation describes the quantum version of the Hamiltonian constraint

and about the Hamiltonian constraint adds...


Parametrization

In its usual presentation, classical mechanics appears to give time a special role as an independent variable. This is unnecessary, however. Mechanics can be formulated to treat the time variable on the same footing as the other variables in an extended phase space, by parameterizing the temporal variable(s) in terms of a common, albeit unspecified parameter variable. Phase space variables being on the same footing.

We introduce \tau as an unphysical parameter labeling different possible correlations between the time reading t of the clock and the elongation x of the pendulum. \tau is unphysical parameter and there are many different choices for it.

Say our system comprised a pendulum executing a simple harmonic motion and a clock. Whereas the system could be described classically by a position x=x(t), with x defined as a function of time, it is also possible to describe the same system as x(\tau) and t(\tau where the relation between x and t is not directly specified. Instead, x and t are determined by the parameter \tau, which is simply a parameter of the system, possibly having no objective meaning in its own right.


Here the expression “classical mechanics appears to give time a special role as an independent variable” also implies that ‘time’ may be a thing that exists, and may be used as an independent variable – i.e. time may be a thing that constantly progresses forwards and this can be incorporated as a variable whose value constantly increments (or some other variation on this).

The statement....

“This is unnecessary, however. Mechanics can be formulated to treat the time variable on the same footing as the other variables in an extended phase space, by parameterizing the temporal variable(s) in terms of a common, albeit unspecified parameter variable.

Suggests theorists are considering the idea that the time variable might be seen as a ‘catalyst’ – ie a ‘common’ but unspecified parameter variable. And that \tau may be used to represent the idea that perhaps we need only consider that things exist, and there velocities etc may be compared, with no 'time' or 'direction of time' being needed in special cases

- While I am suggesting that perhaps there is 'never' such a a thing called time, all cases can be considered without it. (Although the idea of a 'universal clock is undoubtedly useful, if not an essential tool in understanding systems of motion, especially where many moving objects are being understood.)

This suggests that while people may carry out experiments in which they are infact only ever comparing the thing under study to the motion of another thing (eg a ‘clock’) and calling the reading from this thing ‘time’ – or to the idea of ‘the steady passing of a thing called time’ , they may not be fully aware they are just doing this. And that there may be no reason at all to think this extra ‘time’ thing needs to be accounted for, or may have a direction that needs to be explained or explained away.

In simple terms, as the diagram shows, hands on dials can be made to rotate (in any direction), and can be in various locations, and pendulums can be at any point in a swing, and moving in either direction, and these and other things can be compared.

But the idea that there is some other universal thing with a flow and direction to which all things can be compared, or which should be included in equations may just be nothing other than an unfounded idea. (particularly if there is no actual scientific reason or proof that things do not just exist and move in countless directions (And no actual reason or proof to believe that other suggested components of ‘time’ e.g. ‘the past’ actually exist.)

Thus the ‘problem of time’ i.e. the problem of linking apparently directional classical time with apparently bi-directional Quantum Time, may not be a genuine problem but a false problem that arise only with the insistence of the  (possibly) incorrect idea that ‘time’, with or without, a direction may exist.

m.m.

 

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