# B Error in laws of motion

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1. Apr 10, 2016

### 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 cant wrap my head around the concepts. can someone explain for me this phenomenon and why Newton's laws dont explain it?

2. Apr 10, 2016

### PeroK

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.

3. Apr 10, 2016

### Holden Kenne

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.

4. Apr 10, 2016

### PeroK

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.

5. Apr 10, 2016

### phinds

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.

6. Apr 10, 2016

### Holden Kenne

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.

7. Apr 10, 2016

### phinds

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.

8. Apr 10, 2016

### PeroK

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

9. Apr 10, 2016

### Holden Kenne

Well. Better hit the library.

10. Apr 10, 2016

### 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.

11. Apr 10, 2016

### 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.

12. Apr 10, 2016

### Holden Kenne

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?

13. Apr 10, 2016

### ProfuselyQuarky

Yes, of course, energy increases with acceleration.
Inertial mass = the mass of an object as determined by its momentum

14. Apr 10, 2016

### ProfuselyQuarky

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

15. Apr 10, 2016

### Holden Kenne

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

16. Apr 10, 2016

### phinds

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.

17. Apr 10, 2016

### PeroK

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

18. Apr 10, 2016

### ProfuselyQuarky

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.

19. Apr 10, 2016

### Orodruin

Staff Emeritus
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 realise 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.

20. Apr 10, 2016

### Drakkith

Staff Emeritus
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.