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Mr. Swordfish, you wrote ""it would be absurd say it was the other way around, i.e. to insist that you are making the bus speed up by pressing on the back of your seat.""

Did you mean to say, ""it would be absurd say it was the other way around, i.e. to insist that you are creating a force on your back by accelerating."" ?

I think so.  You were making the (good) point that simply reversing F and a in the cause and effect statement seems intuitively absurd in this case.  But the F in statement 1 is the forward force exerted on the back, not the backward force by the back, and the a is the acceleration of the person, not of the bus.

If we make the reversal one of switching equal and opposite forces carefully, we come up with ""The backward force of the back on the bus causes the acceleration of the bus to be lower than it otherwise would be"" which is different than the way you wrote it.  In this case there is no intuitive absurdity at all.  Both cause and effect statements are equally intuitive.

Crowsfoot is right that F=ma, or its fluid dynamics equivalent, doesn't by itself indicate an asymmetric cause and effect relationship.  If causes must precede effects, then we could even argue that F=ma forbids a either causal interpretation, since it refers to instantaneous values of both F and a (and m).  

But its helpful to the reader, I think, to go with the intuitively appealing bias that net forces (pressure differences) cause accelerations (of bodies or particles, or for us, of differential volumes of fluid).  The real difficulty comes when the reader wants to know if the pressure field is caused by the flow field, or vice versa.  We must get him/r to abandon this truly meaningless question, I believe, and understand that Newton's differential equation, and the continuity and mass conservation constraints all have to hold at the same time.  The infinite set of 3d velocity vectors and the infinite set of local pressures have to be consistent with each other, and there is no intuitively meaningful way to say that one causes the other. 

91.103.41.50  

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