No, I mean simply equations that relate functions to their derivatives (of any order): i.e. the mathematical definition of a differential equation. It would perhaps help the discussion if you were aware of some basic mathematical terminology.Differential equations you say? You mean the type of equations, that given the state of the system at any time, the states for all other times may be calculated?
Yet you still believe that science is about modeling known causal relations mathematically, and thus miraculously capturing unknown causal and acausal relations, without being aware of what you are doing.
No, I mean simply equations that relate functions to their derivatives (of any order): i.e. the mathematical definition of a differential equation. It would perhaps help the discussion if you were aware of some basic mathematical terminology. — MetaphysicsNow
First, differential equations themselves do not determine anything. Second, if your point is that all physical laws are time-symmetric, you are not accounting for the Second Law of Thermodynamics. That allows for some time-symmetric solutions where there are no changes in entropy of a system, but where changes in entropy are concerned, we have irreversibility and, yes, there are differential equations (to be specific, partial differential equations) that are used to model entropy changes. — MetaphysicsNow
So, you cannot find a single case where a physical system, whose time-evolution is determined by laws of motion, expressed in differential equation form, is not set for all times given a set of initial conditions.
Of course, given an initial conditionand a terminating condition, the equations of dynamics and thermodynamics will allow you to get from one to the other in either direction by making appropriate reversals to the time-dependent variables and their derivatives, but that was not the question you asked. — MetaphysicsNow
What cluelessness is MetaphysicsNow manifesting? I was under the impression that time-reversal symmetry in physics was precisely the idea that given intial conditions and terminating conditions, you can get from the latter to the fomer by reversing the time-dependent parameters. — jkg20
Initial conditions by themselves don't tell you how things were prior to those conditions, this is the fundamental error you are making. An initial condition at time t involving a ball with constant acceleration a an initial velocity v and an inital spatial location p will determine the forward trajectory of that ball. — MetaphysicsNow
What are you talking about, your reply makes no sense whatsoever? In dynamics, if your system involves a particle in motion, part of specifying the intial conditions for that system is to specify the particle's acceleration and whether or not it is constant. — MetaphysicsNow
Have you ever actually done any physics rather than just talking about it? — MetaphysicsNow
OK, so you are talking about Langrangian-Hamiltonian mechanics, whereas my example was expressed in the context of Newtonian mechanics. — MetaphysicsNow
Also I don't know what Tom means when saying that the acceleration is "captured" by the Hamiltonian. The canonical coordinates of the Hamiltonian formalism are position and momentum. Maybe Tom means that the time derivative of momentum in Hamilton's equations reduces to the second law? — Uber
Newton's second law is one formalism that specifies the dynamics of a classical system. It is a second-order differential equation. To solve it you need the position and velocity of a system at some given time t. You do not have to specify acceleration to solve the second law. — Uber
Between Newtonian and Hamiltonian mechanics? Depends what you mean by fundamental. But in any case there is a difference in the tools they provide to solve problems. But all of that is irrelevant to the dispute about time-reversal symmetry.You think there is a fundamental difference?
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.