# Current status of Newton's Third Law of Motion

Hi,

I was wondering, what is the status of Newton's Third Law of Mechanics in modern physics? I'm told that it does not always hold. In that case, when and how does it break down? Thanks.

Molu

Related Other Physics Topics News on Phys.org
loom91 said:
Hi,

I was wondering, what is the status of Newton's Third Law of Mechanics in modern physics? I'm told that it does not always hold. In that case, when and how does it break down? Thanks.

Molu
Well, Newton's Third Law is a concept that is both defined and valid in classical physics. So this law always holds.

However, when going to special relativity the third Newton Law is also valid. Beware that we are talking about F = dp/dt here and NOT F=ma. After the calculation of the dp/dt term, you shall see that force is no longer parallel to acceleration in special relativity. The reason for this is the presence of the Lorentz factor (the gamma) in special relativity. This factor contains a v²-part in the denominator that is also dependent of time.

regards
marlon

Does it also hold in classical fields? What about quantum fields?

But this law is not defined for quantummechanical phenomena. For example, when you use concepts like acceleration or velocity you need to know how an object's orbit varies with time (this is essentially what velocity is all about). This clearly contradictis with the HUP.

Just to be clear, i did not say the F = dp/dt is wrong in the case of QM. What i say is that this law is NOT DEFINED for QM-theory.

marlon

In case you're wondering, <dV/dx>=-d<p>/dt in QM, which is the same thing as saying that <F>=d<p>/dt, so it is true in a sense.

Manchot said:
In case you're wondering, <dV/dx>=-d<p>/dt in QM, which is the same thing as saying that <F>=d<p>/dt, so it is true in a sense.
But that's the second law, what about the Third? And also, does the third law work for classical fields (Maxwell/Einstein)? Thanks.

Molu

Manchot said:
In case you're wondering, <dV/dx>=-d<p>/dt in QM, which is the same thing as saying that <F>=d<p>/dt, so it is true in a sense.
No that is very much untrue for several reasons. First of all, you are working with observables here and nut just p, a or F vectors. Secondly, haven't you read my remark on the violation of the HUP ? Doesn't that count ?

marlon

It is true newton's third law is made for classical physics like Bohr's theory etc. but as bohr's theory is evolve or redifined by quantum physics you can also state third law in qm's language. what you have to do is to take account of changes occur at atomic level in a body when it is in acceleration or under the influence of any type of force.
Over all I think Newton' s third law is valid in qunatum mechanics (whether we don't know it fully or not).

For those saying the third law works in QM: how do you define the force on a wavefunction?

Since Newton's laws deal with dynamics we need to work with wavefunctions satisfying the time-dependant Schroedinger equation, so for example the wavefunction is a time-evolving superposition of constant momentum eigenstates? How do you find dp/dt of this?

I don't want to rule it out because of the uncertainty principle alone, since we can work with momentum and have no need for position- and the energy/time relation is not so clear cut in my head since time is not an observable like energy.