Q&A

# Why we can't find a particle accelerating unless there's some other particle accelerating somewhere else?

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I was reading "Introduction to classical Mechanics" by David Morin. In that book they wrote that

The third law says we will never find a particle accelerating unless there’s some other particle accelerating somewhere else. The other particle might be far away, as with the earth–sun system, but it’s always out there somewhere.

But, when we are walking, running. We are accelerating. Even, vehicles are accelerating also. But, why the definition says,"we can't find a particle accelerating ......." Seems like they talking about QM (I am not sure) cause, in "Classical" World I can see everything accelerating but, they had talked about particle which means they are referring to Quantum World. It's looking like Quantum Entanglement cause, when a particle (big object) is far away than, they can't contact in Classical World but, if we think of QM than, they can contact (That's why I am referring to QM).

$$\frac{d_{Ptotal}}{dt} = \frac{dp_1}{dt} + \frac{dp_2}{dt}$$

They wrote the above equation. Then talked about above definition. What I understood from the equation that is,"We can't find a particle accelerating cause, a particle always (not in Quantum World) has equal of negative force so, until two particles contact each other their momentum is forever $0$"

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If you are accelerating while running on Earth, actually you are also accelerating Earth in the opposite direction. However for a given force, the acceleration is inversely proportional to mass, therefore when some $60\,\rm kg$ person accelerates by, say, $1\,\rm m/s^2$, then Earth, which has a mass of about $6\cdot 10^{24}\,\rm kg$, will only accelerate with $10^{-23}\,\rm m/s^2$, far to low to actually notice (if accelerating for a second, the change of speed of the Earth will be so that in about three years it moved by the diameter of a proton — provided you kept running at the final speed in the same direction for the whole three years).

Basically, we can ignore the effect our motion has on the motion of the Earth because the Earth has such a large mass. But in the end, those effects are there. And yes, that means everyone of us is moving Earth around a little bit all the time. It's just that this movement is too small to actually matter.

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The third law says we will never find a particle accelerating unless there’s some other particle accelerating somewhere else. The other particle might be far away, as with the earth–sun system, but it’s always out there somewhere.

This was probably embedded in more context. It seems the point he is trying to make is that for one object to accelerate, it must push on some other object. Therefore, that other object must also be accelerating.

When a rocket is accelerating in space, it causes propellant to accelerate in the opposite direction. When you start running on earth, you push on the planet, which accelerates very slightly in the opposite direction. Even if you're using a solar sail in space, the photons hitting the sail accelerate in the opposite direction. Since photons have finite energy, they have finite momentum. The momentum is being swapped between the photons and the sail to push the spacecraft.

In all the examples above, the total momentum was conserved if you examine a bubble large enough to encompass both objects completely.

Another way to paraphrase this is that you can't accelerate without pushing on something else. That something else will therefore also accelerate, although in the opposite direction. The total momentum is conserved.

Olin photons can't accelerate like most of the objects because photons always move with one speed for all inertial frames.

I was over-simplifying because this level of detail was not relevant to the question. Yes, photons don't change their speed, but they still have momentum that gets transferred to any object they bounce off of or are absorbed by.

Their speed may not change, but their velocity (speed in a specific direction) certainly can. You can use that change in velocity to compute an effective acceleration, even if the speed doesn't change.

Hopefully this digression didn't confuse the point of the OP's actual question too much.

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But, when we are walking, running. We are accelerating.

Wrong.When you are walking you're moving at a costant speed.

The third law says we will never find a particle accelerating unless there’s some other particle accelerating somewhere else

The book says that because of Netwon's 3rd law which says that forces only come in pairs , for each action there is a reaction.

If two marbles collide then during the contact a force will be exerted on each marble , the one being the reaction of the second force.But those account as internal forces so the total change in momentum of the system is 0.

Hope this helps.

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