Understanding Newton's Laws of Motion: Exploring Errors and Contradictions

[Holden Kenne]

Hi, I'm a frehshman in High school writing a paper about Isaac Newton. One of my paragraphs is about the laws of motion. I came across a tidbit of information - there are instances in which Newton's laws are not correct. One example I found was that, at speeds approaching that of light, an objects mass will increase, which contradicts Newton's Second law. I've tried to read about general and special relativity but i just can't wrap my head around the concepts. can someone explain for me this phenomenon and why Newton's laws don't explain it?

 

[PeroK]

Hi, I'm a frehshman in High school writing a paper about Isaac Newton. One of my paragraphs is about the laws of motion. I came across a tidbit of information - there are instances in which Newton's laws are not correct. One example I found was that, at speeds approaching that of light, an objects mass will increase, which contradicts Newton's Second law. I've tried to read about general and special relativity but i just can't wrap my head around the concepts. can someone explain for me this phenomenon and why Newton's laws don't explain it?

Isaac Newton knew nothing about Special or General relativity. So, if you're writing about Newton, why worry about relativity, which came along 200 years after he died?

If you start looking at relativity, then you'd better change the subject of your paper from Newton to Einstein.

 

[Holden Kenne]

Isaac Newton knew nothing about Special or General relativity. So, if you're writing about Newton, why worry about relativity, which came along 200 years after he died?

If you start looking at relativity, then you'd better change the subject of your paper from Newton to Einstein.

The reason I was reading about relativity is because I read that, at the time of the publication of Philosophae, Newton did not take account for speeds reaching that of near-c. I just want to understand why they don't.

 

[PeroK]

The reason I was reading about relativity is because I read that, at the time of the publication of Philosophae, Newton did not take account for speeds reaching that of near-c. I just want to understand why they don't.

He had no idea that the speed of light was anything special. If he were magically brought back to life now, he would not have the faintest idea what we are talking about. He studied light and knew its speed.

 

[phinds]

The reason I was reading about relativity is because I read that, at the time of the publication of Philosophae, Newton did not take account for speeds reaching that of near-c. I just want to understand why they don't.

He DID take into account speeds near c, he just didn't know that his method was wrong for them.

Einstein discovered over 100 years ago that Newtonian gravity is only a subset of the more General Relativity. That is, GR give exactly the same results as Newton (well, it does to a lot of decimal places) at slow speeds and away from extremely strong gravitational fields such as that around a black hole.

If you want to know more, you HAVE to read about General Relativity.

 

[Holden Kenne]

He had no idea that the speed of light was anything special. If he were magically brought back to life now, he would not have the faintest idea what we are talking about. He studied light and knew its speed.

I know he studied light and optics. I just would like to know why Newton's second law doesn't apply at speeds reaching that of light.

 

[phinds]

I know he studied light and optics. I just would like to know why Newton's second law doesn't apply at speeds reaching that of light.

I say again, If you want to know more, you HAVE to read about General Relativity, although you should probably start with Special relativity since that only requires high school algebra.

 

[PeroK]

I know he studied light and optics. I just would like to know why Newton's second law doesn't apply at speeds reaching that of light.

Newton's laws don't apply to Quantum Mechanics either. So, you better learn about that as well.

 

[Holden Kenne]

I say again, If you want to know more, you HAVE to read about General Relativity, although you should probably start with Special relativity since that only requires high school algebra.

Newton's laws don't apply to Quantum Mechanics either. So, you better learn about that as well.

Well. Better hit the library.

 

[ProfuselyQuarky]

True mass does not change when velocity increases. Mass has nothing to do with observer’s frame of reference or speed or anything of that sort.

Nothing can be accelerated to the speed of light—that’s the ultimate “speed limit”. However, the faster an object's velocity becomes (approaching, but never reaching, the speed of light), their energy, inevitably increases. Their inertial mass is increasing. Relativistically speaking, mass and energy are equivalent. In this way, mass is added when energy is added and mass is lost when energy is lost.

The definition of mass used by Newton and the definition of mass used by Einstein aren’t exactly the same thing.

Of course, I'll probably be corrected in some way or another for whatever I just said.

 

[phinds]

It is now deprecated to say that an object's mass increases as it approaches c since that isn't really what happens; rather, say that it's stress-energy tensor increases.

 

[Holden Kenne]

True mass does not change when velocity increases. Mass has nothing to do with observer’s frame of reference or speed or anything of that sort.

Nothing can be accelerated to the speed of light—that’s the ultimate “speed limit”. However, the faster an object's velocity becomes (approaching, but never reaching, the speed of light), their energy, inevitably increases. Their inertial mass is increasing. Relativistically speaking, mass and energy are equivalent. In this way, mass is added when energy is added and mass is lost when energy is lost.

The definition of mass used by Newton and the definition of mass used by Einstein aren’t exactly the same thing.

Of course, I'll probably be corrected in some way or another for whatever I just said.

So, what I gather from this is that, whether an object's velocity is 10km/h or 10,000 km/s, mass doesn't change, but energy does? And inertial mass = force needed to move an object at x speed?

 

[ProfuselyQuarky]

So, what I gather from this is that, whether an object's velocity is 10km/h or 10,000 km/s, mass doesn't change, but energy does?

Yes, of course, energy increases with acceleration.

And inertial mass = force needed to move an object at x speed?

Inertial mass = the mass of an object as determined by its momentum

 

[ProfuselyQuarky]

It is now deprecated to say that an object's mass increases as it approaches c since that isn't really what happens; rather, say that it's stress-energy tensor increases.

Yeah, that's a more of correct way to say it.

 

[Holden Kenne]

Yeah, that's more of a correct way to say it.

could you explain in layman's terms what stress-energy tensor is?

 

[phinds]

So, what I gather from this is that, whether an object's velocity is 10km/h or 10,000 km/s, mass doesn't change, but energy does? And inertial mass = force needed to move an object at x speed?

It takes energy (LOTS of energy) to get an object up to near-c speeds so yes, it has more energy.

Think about this: "speed" is a concept that is only meaningful in a relative way. That is, ALL motion is relative.

You, right now as you read this, are moving at .9999999+c according to a particle in the CERN accelerator. Do you feel any heavier?

If you and the particle were to start off at the same place, motionless relative to each other, and you were to be accelerated away from the particle to near-c, then several things would be true. First, if the acceleration were similar to that experience by the particle in the accelerator, you would be a thin red paste but we'll skip over that one. YOU would not feel this slightest bit different but the particle would "see" you as being massively time dilated and your wristwatch would be ticking away at an incredibly slow speed to it (but to you it would be ticking away at one second per second). You would also be massively length contracted down to hardly any length at all in the direction of your travel (but you would notice nothing amis).

You HAVE to read about Special Relativity to "get" all this. It's not going to be very helpful to you to try to figure it all out by asking random questions on an internet forum. Go read and when you get to something you don't understand, you'll have some context to come back here and ask questions.

 

[PeroK]

could you explain in layman's terms what stress-energy tensor is?

The stress-energy tensor was discovered by Isaac Newton in 1696 while researching ...

 

[ProfuselyQuarky]

could you explain in layman's terms what stress-energy tensor is?

A tensor is an "object" that describes the linear relationships between scalars and vectors and geometry (surely you know what those are). Stress-energy tensor is the quantity describing momentum, dentistry, and the flux of energy in spacetime all in one. It can describe radiation, fields, and, in this case, matter.

 

[Orodruin]

I honestly think bringing tensors into the discussion is very much overshooting as the OP is a high-school freshman (I have relabelled the thread "B" accordingly). Please keep the discussion at the OP's level.

OP: You do not need to learn relativity or quantum mechanics to understand Newtonian mechanics as Newton understood them. As you learn more and more physics, you will come to realize that the theories that have evolved throughout the years have a limited scope of applicability, but they still work very well within that scope. I do suggest you focus on your chosen subject rather than digging deeper (for now) into when the theory breaks down.

That being said, Newton's second law works perfectly fine in relativity, but it needs to be constructed in the proper relativistic way in order to have the correct properties. It is not obvious how the relativistic version should look like as there are some things in the law which could generalise to the relativistic setting in different ways.

 

[Drakkith]

It's might be more accurate to say that Newtonian Mechanics (mechanics based on the laws of physics known prior to Special and General Relativity and Quantum Physics) does not work well at speeds approaching the speed of light or in regions of extremely high gravitational fields. Newton's laws of motion still apply in newer theories, they are just expressed differently as far as I know.

 

[Markus Hanke]

I know he studied light and optics. I just would like to know why Newton's second law doesn't apply at speeds reaching that of light.

Newtonian mechanics is built on the assumption that there is a universally applicable notion of time, which all observers share, and that this is separate from the concept of space. Specifically, it relies on a common concept of simultaneity, which everyone shares. We know now that this works fine as an approximation for low velocity type of situations, but in reality the universe is constructed differently - space and time are on equal footing, and neither one on its own is absolute and the same for all observers. What's more, if you combine time and space into spacetime, you will find that the resulting construct has a geometry that is different from the usual Euclidean geometry you would have studied in school; the difference is largely irrelevant at slow speeds, but it becomes significant once you approach the speed of light ( or go into a strong gravitational field ). That is why Newton's laws are not guaranteed to work outside their domain of applicability ( low-velocity, low-energy situations ).

 

[votingmachine]

I know he studied light and optics. I just would like to know why Newton's second law doesn't apply at speeds reaching that of light.

It is not really necessary to know why ... the fact is that Newton's laws of motion don't work in all situations. Those situations are uncommon ones. Newton lived in a time without cars. A fast race horse might hit 25 mph. The speed of light is 670,000,000 mph. Newton did not have a digital stopwatch or a digital clock ... I'm not really sure that he had anything all that accurate.

What Newton came up with, was a set of simple laws of motion that were very nearly universally accurate for everything that Newton applied them to.

I don't see it as a "why" question. Why is something what it is? It just is what it is. Newton's models are not universally accurate, they are conditionally accurate. As most of us are likely to only find the conditions that they are accurate ... they should be learned well.

I will extemporize, without quite knowing. I think Newton would have thought that light had a speed of origination, but that it was not a limit, just a very large number. So a ball thrown from a moving boat, has the additional velocity of the boat. Likewise, a light shining from a boat, would be expected to have the additional velocity of the boat. If you measured light emitted from the shore in that boat, it was a trifle slower than light from the boat. As far as I know, everyone thought just that until the Michaelson-Morley experiment shook things up, by changing the understanding of the motion of light. Every experiment shows that light has the same velocity, whether measured from a galaxy receding rapidly, or from an advancing car headlight. That was a profound deviation from Newton.

Newton's laws don't predict the motion of things that are traveling very fast. The reason is that the universe works like that, not like Newton predicted, but could never really test. Einsteins laws of motion do work at those unusual conditions, in addition to working at ordinary conditions.

 

[haushofer]

I think the modern view is not that Newton's theory is 'wrong'. Every theory which is written down comes with a domain of validity. Newton's mechanics is valid (is approved by experiments) for certain velocities/energies. But for velocities comparable to the speed of light, it turns out that Newton's ideas (about absolute space and time) are merely approximations of a more complete view, namely the one of Einstein.

We now also know that Einstein's theory of special and general relativity is probably incomplete. So there is a supertheory out there which suplements Einstein's theory.

Hope this helps.

 

[votingmachine]

As I understand it, the two formulas can be written:
Newton's:
F=ma
and Einstein's:
F=ma(1/sq.rt(1-(v^2/c^2))

That difference between the two is the Lorentz factor which is almost 1 for any "ordinary" speed. So at any speeds that Newton might encounter the formula was:

Force equals mass times acceleration times 1

This wikipedia page has a nice chart of the Lorentz factor and when it starts to matter:

https://en.wikipedia.org/wiki/Lorentz_factor

Even at a speed one tenth of light speed, the formula is:

Force equals mass times acceleration times 0.995

It is unfortunate that Newton was not correct. If it was always F=ma, we could theoretically build a spaceship that went faster than light. (That is of course JMO, that FTL travel being impossible is unfortunate.) Instead at the light speed limit, additional force applied does not result in additional acceleration. The energy ends up adding to the conserved energy of that system, most simply thought of as mass increasing, as you phrased it in the OP, but that simplified thinking is TOO simple and should be avoided.

The reason I was reading about relativity is because I read that, at the time of the publication of Philosophae, Newton did not take account for speeds reaching that of near-c. I just want to understand why they don't.

I think Newton probably considered his equations to be valid under all circumstances. There was no reason to guess that speeds near light mattered. As a bad analogy, I might say that I think chocolate would taste good on Pluto, because the law that chocolate tastes good seems to validly generalize. We generalize rules until they break down. There just was no way for Newton to encounter a situation where they broke down enough to not consider them likely to be universally applicable.

So it is not that Newton did not take into account speeds near light, but that he had no reason to expect that special consideration needed to be taken for any speed. I have no reason to expect chocolate to taste different on Pluto, so I regard the chocolate taste rule as a general one.

 

[Ibix]

and Einstein's:
F=ma(1/sq.rt(1-(v^2/c^2))

No - the formula depends on the direction of the applied force relative to the velocity of the object, and varies between $F=\gamma ma$ and $F=\gamma^3ma$. Also, in general, the acceleration is not parallel to the force.

 

[Dale]

I know he studied light and optics. I just would like to know why Newton's second law doesn't apply at speeds reaching that of light.

Objects with mass cannot reach or exceed c. So if I have a 1 kg object traveling at c-1 m/s, and I apply 1N force, then by f=ma I expect that it will accelerate to c in 1 s.

This is not how physics near c actually works, but Newton had no reason to expect that.