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Lamarr
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I was just thinking, are Newton's laws of motion most fundamental, or can they be reduced to something even simpler?
Lamarr said:I was just thinking, are Newton's laws of motion most fundamental, or can they be reduced to something even simpler?
I think they can be derived from more general principles. Whether that makes them simpler or not, depends on your point of view.Lamarr said:I was just thinking, are Newton's laws of motion most fundamental, or can they be reduced to something even simpler?
Andrew Mason said:I think they can be derived from more general principles. Whether that makes them simpler or not, depends on your point of view.
It can be shown that Newton's second and third laws follow from the concept of Galilean relativity: 1. that all inertial frames of reference are equivalent in the sense that the laws of physics are the same to all inertial observers and 2. that time and distance are measured to be the same by all observers.
With these principles, you can derive the second and third laws of Newton. Or you can start with Newton's laws (and the assumption that time and distance are the same to all observers) to derive the principles of Galilean relativity.
AM
Lamarr said:But where does "equal and opposite" come from in Galilean relativity?
Does the 3rd Law still hold true in Special Relativity?
Andrew Mason said:I think they can be derived from more general principles. Whether that makes them simpler or not, depends on your point of view.
It can be shown that Newton's second and third laws follow from the concept of Galilean relativity: 1. that all inertial frames of reference are equivalent in the sense that the laws of physics are the same to all inertial observers and 2. that time and distance are measured to be the same by all observers.
With these principles, you can derive the second and third laws of Newton. Or you can start with Newton's laws (and the assumption that time and distance are the same to all observers) to derive the principles of Galilean relativity.
AM
Galilean relativity follows from the third law. So if you go backward and assume Galilean relativity as a premise, the third law follows.Lamarr said:But where does "equal and opposite" come from in Galilean relativity?
The conservation of momentum does hold. But the concept of simultanaeity disappears. Absolute simultanaeity is implicit in the third law. Since the times of interaction are not the same between interacting bodies moving at relativistic speeds, the forces are not equal and opposite same so the third law does not hold in SR.Does the 3rd Law still hold true in Special Relativity?
You could google "galilean relativity". You will find discussion of Galilean relativity following from Newton's laws but you will have a difficult time finding anyone who discusses the reverse connection.aaaa202 said:Wow, I would like to see those derivations - I never knew that was possible. What should I search for?
Andrew Mason said:The conservation of momentum does hold. But the concept of simultanaeity disappears. Absolute simultanaeity is implicit in the third law. Since the times of interaction are not the same between interacting bodies moving at relativistic speeds, the forces are not equal and opposite same so the third law does not hold in SR.
AM
If you are talking about balls and boxes, you would be right - although the distance between interacting surfaces is not zero - just very small. Any "collision" involves atoms interacting through electrical forces at a distance.Vorde said:I'm not sure I follow this.
If we are talking about the kinds of interactions that basic physics classes talk about (balls and boxes and the like), wouldn't any interaction require the distance between the interacting objects be zero, and therefore wouldn't the times of interaction be equal regardless of reference frame?
It does if you are careful about how you define forces and acceleration. A better statement would be that momentum is still conserved in Special Relativity. So if you define forces via dp/dt, 3rd law must hold.Lamarr said:Does the 3rd Law still hold true in Special Relativity?
I disagree. Galilean relativity is a consequence of Newton's first law (inertial frames exist) and Newton's second law (F=ma; force and acceleration are frame invariant). Not the third law. That is a beast of a quite different color.Andrew Mason said:It can be shown that Newton's second and third laws follow from the concept of Galilean relativity: 1. that all inertial frames of reference are equivalent in the sense that the laws of physics are the same to all inertial observers and 2. that time and distance are measured to be the same by all observers.
But you would have to measure momentum, force and time all in the same frame of reference. Newton's third law would apply if you did that. But Newton's third law talks about the force of A on B and the force of B on A being equal. If these forces are measured in the respective reference frames of each body, they will necessarily differ because time measurements will differ between frames.K^2 said:It does if you are careful about how you define forces and acceleration. A better statement would be that momentum is still conserved in Special Relativity. So if you define forces via dp/dt, 3rd law must hold.
That is one way of looking at it. One could also say that Newton's first and second law PLUS the premise that time and distance measurements are equal will lead to the third law. Then one could say that the second and third laws (with that premise) imply Galilean relativity.D H said:I disagree. Galilean relativity is a consequence of Newton's first law (inertial frames exist) and Newton's second law (F=ma; force and acceleration are frame invariant). Not the third law. That is a beast of a quite different color.
I agree that the conservation of momentum is fundamental. However, it is not just Newton's third law that fails to hold if force transmission is not instantaneous. The second also does not hold. The second law implies that masses of bodies do not change in an interaction. However, if forces at a distance do not act instantaneously, the conservation of momentum requires, as SR provides, that energy carries momentum. As a result, when a collision is measured in a single inertial reference frame (e.g. the centre of mass frame), mass is transferred between bodies due to the transfer of energy.Newton's third law is a true law of physics. It's empirical, it's not always true, and it can be derived from deeper concepts. Those deeper concepts are conservation of linear and angular momentum. Newton's third law assumes that individual forces can always be paired and that force transmission is instantaneous (action at a distance). With multi-body forces such as the chiral three-nucleon forces in a helium nucleus you don't get Newton's third law. If the force transmission isn't instantaneous, the field that mediates the force will itself contain linear and angular momentum, and Newton's third law once again fails to be true.
All I am saying is that Galilean relativity is an even simpler form. Newton's laws flow from the premises of Galilean relativity: if it were not the case that F=ma or if interaction forces were not equal and opposite, (assuming time and distance measurements to be the same in all frames of reference) Galilean relativity would be violated.With those simplifying assumptions, conservation of linear momentum yields the weak form of Newton's third law, that forces exerted by a pair of interacting particles on one another are equal in magnitude but opposite in direction. Adding conservation of angular momentum yields the strong form of Newton's third law, that forces exerted by a pair of interacting particles on one another are equal in magnitude but opposite in direction, and are directed along the line connecting the two particles.
There's something even deeper than the conservation laws, and that's Noether's theorems. However, the conservation laws (and even deeper, Noether's theorems) aren't simplifications of Newtonian mechanics. They're more complex. Newton's laws are the simple form.
The interaction times are not the same for all the interactions.aaaa202 said:Andrew Mason: I don't like your derivation of the third law from Galilean relativity. Suppose that we have a system of three particles A,B,C. Then the condition that the momentum is conserved in the system is as you say:
(Fab+Fac+Fba+Fbc+Fca+Fcb)*dt=0
But I don't see how setting Fxy = -Fyx is the only solution to that equation. How about for instance: Fac = -Fab, Fba=-Fbc,Fca=-Fcb? why couldn't I assume that. It would be a wicked world yes, but I don't see a problem with it.
Yes, Newton's Laws of Motion can be simplified in certain cases. The three laws can be applied to most situations involving motion, but they may not always provide the most accurate prediction of motion. In such cases, more complex theories such as Einstein's theory of relativity may be needed.
One way to simplify Newton's Laws of Motion is by applying them to idealized, simplified situations. For example, instead of considering all the forces acting on an object, we can focus on one or two major forces to simplify the analysis. Another way is to use mathematical models and equations to represent motion, which can make the application of the laws easier.
Yes, many real-life examples of motion can be simplified using Newton's Laws. For instance, the motion of a ball rolling down a hill can be analyzed using just the force of gravity and the ball's mass, neglecting other smaller forces such as air resistance. Similarly, the motion of a satellite in orbit around the Earth can be described using just the force of gravity and the satellite's mass.
Yes, there are limitations to simplifying Newton's Laws of Motion. The laws may not accurately predict the motion of objects in extreme conditions, such as at very high speeds or in very strong gravitational fields. In such cases, more advanced theories may be needed to fully describe the motion.
Simplifying Newton's Laws of Motion allows for easier understanding and application of these fundamental principles of physics. By simplifying complex situations, we can gain a better understanding of the basic concepts and use them to make predictions about motion in the real world. Additionally, simplified versions of the laws can be used to teach students the basics of physics before moving on to more advanced topics.