# Does Newton's first law of motion contradicts causality?

First, English is not my mother tongue and hence maybe the expressions I will use are not very accurate.

Causality as I understand is when there is a change, then there is a preceding event "caused" that change to occur.

If I understand right then I think that Newton's first law of motion contradicts causality as I understand.

The law says that in absence of any force, the object is unaccelerated.

The problem is, if an object moves with a constant velocity in a straight line, then there is a "change" in it's position and hence requires a "cause" to keep that change occuring.

Did I miss something?

• The issue is that for Newton (and Descartes) uniform motion is NOT change (as per Aristotle) but a "steady state". Commented Sep 20, 2022 at 13:50
• In addition to what @MauroALLEGRANZA said, there is also the issue that in come cases an object can be the cause of its own change. Commented Sep 20, 2022 at 15:35
• @MauroALLEGRANZA thanks for your comment, but can we actually say that there is no change? Commented Sep 20, 2022 at 17:54
• @DavidGudeman do you mean that the inertia/mass of the object is the cause of that change? Commented Sep 20, 2022 at 17:55
• Indeed there's something of philosophical import here in your case, does the constant velocity cause the change of position as practically understood in everyday life or, per definition of velocity as the derivative of position w.r.t. time in classic calculus, does the (rate of) change of position cause such a uniform velocity?... Commented Sep 21, 2022 at 2:26

First, responses that uniform motion is not change, but rather a steady state, miss the point. That's only true if there is only a single particle in the universe. If there are two particles moving in different directions, then the distance between them will change over time, despite no force being exerted, and this changing distance is a fact that cannot be explained away by selecting a different inertial frame.

(Yes, you can't tell which of the two particles is moving and which is stationary. That doesn't matter. The distance between them is changing over time at the same rate according to Newtonian physics, regardless of which you take to be moving and which you take to be stationary.)

So yes, with Newton's first law there can be change without any force being exerted. However, this is not acausal change. The cause of change is the position and velocity of each particle a moment previously; this determines, and causes, the position and velocity of each particle a moment later. For example, if a particle is at position x with velocity v at time 0, and no force acts upon it, then at time t it will be at position x + vt. And the cause of it arriving at position x + vt at time t, is that it was previously at position x with velocity v at time 0.

To put it another way, a cause is not necessarily a force exerted, but can be any property of a physical system at a certain time, that leads the system to have a second property at a later time.

• I want to thank you a lot for your answer. But, - thanks to @Double Knot - the definition of velocity is the rate of change in position, or the derivative of position w.r.t. time. So it's a dependent quantity on position. If that is right, I think it shouldn't be the cause of the next position. Commented Sep 21, 2022 at 8:53
• @MohamedMostafa In Newtonian dynamics the velocity is a separate quantity from the position. It really has to be if you want to talk about the state of a system at a certain time; it's not enough to list the position of all of the particles in the system, because "a ball at position 1,1 moving up" is a different state from "a ball at position 1,1 moving down." You also have to say what directions they are moving and how fast, or equivalently their momentum. Commented Sep 21, 2022 at 9:12
• @MohamedMostafa See phase space "a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usually consists of all possible values of position and momentum variables." Commented Sep 21, 2022 at 9:18
• It is also true that velocity is the derivative of position, but we must treat it as a separate variable when speaking of the state of a system. Commented Sep 21, 2022 at 9:21

The problem is, if an object moves with a constant velocity in a straight line, then there is a "change" in it's position and hence requires a "cause" to keep that change occuring.

The thing is physically constant movement is indistinguishable from being at rest. That might sound counter intuitive but picture yourself doing a physical experiment and picture yourself doing that same experiment within a train. As long as the train is not accelerating or slowing down you'll have the same results as if you were at rest. You can go further and imagine taking sleeping pill and entering a black box and you can't even tell if that box is moving or standing still.

So for all intents and purposes you could physically take the perspective that it's not actually you that is moving but that you are standing still and that the world is moving around you. That constant velocity is not an absolute property but only a relative one between systems at rest. And so there might not actually be a change in your position at all.

• Let's rewrite the problem as two particles with two different constant velocities. The relative position IS changing, so what is the "cause" of this change if there is no force applied? Commented Sep 20, 2022 at 17:53
• Finally I see why going around a circle is called 'accelleration': inside the train traversing a bend, the experiment would go pear-shaped. Commented Sep 20, 2022 at 18:21
• @MohamedMostafa Perhaps think of it like moving on a slippery surface: it takes force to speed up, and force to slow down, but in between, you are just coasting, no force. Relative motion is an illusion: imagine that the other object explodes or vanishes. Now where did 'your' motion go? It was never there. Commented Sep 20, 2022 at 19:28
• @MohamedMostafa Yes the relative velocity is changing but each of them could say that relative velocity is the velocity of the other particle. If you have no absolute frame of reference you could treat constant velocity as being at rest, which is why such systems are called "inertial frame of reference". Commented Sep 21, 2022 at 6:40
• You might even have experienced that if you're riding trains and sit in one in a train station and the train on the other track starts moving and you think it's your train that is moving until it passes you and you see the environment being at rest again. That illusion even works if you are fully aware of it! Like you could look out of the other window and see yourself being at rest and then try it again and it will still work. Despite you being at rest (even by the standard of what we colloquially call "at rest", so not just imagining yourself being at rest). Commented Sep 21, 2022 at 11:39

In Newtonian mechanics the law of causality can be stated in the following very precise form:

• If one knows the current position and the current momentum of a particle, then one can compute its position and momentum for all future and all past time points.
• In particular, if no force acts on the particle then its velocity remains constant.

These results follow by easily solving Newton's differential equations in this very specific case.

• Prediction doesn't imply causation. If one is in the desert and see some animal, they predict that there is a near source of water. But, the presence of animal is not the cause of water. A second problem is with the attached definition, if a particle is at rest on a rough surface. You can't predict if it was moving in the past or at eternal rest. And you can't predict neither it's direction of moving in the past nor it's initial position or speed. Commented Sep 21, 2022 at 9:05
• Also, according to this: sites.pitt.edu/~jdnorton/Goodies/Dome there is a deeper problem in differential equations of Newton's mechanics. Commented Sep 21, 2022 at 9:09