In classical mechanics the coordinates of a particle are functions of time. That path is a solution of the equations of motion. In principle then it is just a parameter and can be eliminated giving a direct relation between the coordinates E.g. If you do this for a particle subject to uniform downward acceleration you obtain the upside down parabolic relation of x with y. No time. So is time really necessary?
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4Possible duplicate of What is time, does it flow, and if so what defines its direction? – John Rennie Sep 26 '17 at 16:19
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See also Is there a proof of existence of time? – John Rennie Sep 26 '17 at 16:19
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4If my friend and I both go to the bus station and then leave, but possibly at different times, how can you tell if we actually met, without invoking time? – knzhou Sep 26 '17 at 16:23
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For the record I think the downvotes are unwarranted. It's a duplicate, but it's still a perfectly good question. The question is alluding to the idea of the block universe, which as it happens I subscribe to myself. – John Rennie Sep 26 '17 at 16:36
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Ask Julian Barbour, https://en.m.wikipedia.org/wiki/Julian_Barbour, he would agree with you. Personally, I am not sure this is a physics question, and that any answers will reflect the fact that the variable t is very useful in mathematical terms, but physically hard to explain. – Sep 26 '17 at 17:08
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I think it is a very good question. A mechanics without time! – peterh Sep 27 '17 at 20:36
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While some equations that contain an explicit time coordinate could be reformulated in a way that doesn't explicitly reference time, I believe this is missing the broader point about why time matters. Arguably, the purpose of physics (and science more generally) is to create a framework by which we can understand, and make testable predictions about, the physical world. We, as humans, care about when things will happen, and so we often want our predictions to include a component of "when". Moreover, the information available to us is often the state of things at a certain time (i.e., the initial conditions), which introduces time into the problem.
If I throw a ball in the air, I don't just want to know what path it will follow - I want to know when it's coming back down. Wouldn't you?
Tim Goodman
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1If you ask this question to the average jo in the street he would regard you as crazy to doubt it. – Robbydcm Sep 27 '17 at 11:15
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Take a three dimensional map. If all the derivatives (dx/dy, dy/dz, dz/dx) were zero it would just be a flat land with no information. Without time even nonzero derivatives have a unique information fixed for ever on this map, life cannot be described, as no change ever. Introducing a dx/dt, etc allows for changes in the map including finally life.
anna v
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