# How can an object move in a straight line?

1. Jan 4, 2016

### callmespitfire

I get the conservation of momentum law that states that objects always have conserved momentum. I can easily accept this with the view that while an object appears to be at rest it is actually speeding through the universe at a massive speed. I just have the same speed so relative to myself the object is "not moving". A problem arises when I try to visualize the 'straight lines' part. It is impossible for something to move in a straight line. No matter how I visualize it, this straight line motion does not match my world and it drives me crazy sometimes.
Anyway, picture an object moving in a 'straight line' on earth. It can't, because earth is rotating. So go to the pole and chuck something up in a 'straight line'. It's not straight because the earth is orbiting. What isn't orbiting? the earth is orbiting it own center of gravity if we think about it. Everything has conserved angular momentum, everything must curve.
The only place I can envision a straight line is through the 'axis' of the universe if it has one. However, the thought of approaching the axis of the universe evokes images of massive speeds due to the 'centripetal force' of moving closer to the axis of rotation from a point moving outwards.
I have always been fascinated by physics but I have always been scared of the maths. I struggle to find relation between mathmatical operations and my world. Time/motion, how does this relate? Why is physics defined as the study of matter and energy and not time? What does addition and multiplication actually represent in terms of motion?
I'm trying to learn the maths but I get sucked into forgetting the distinction between maths and physics. How does something like an exponent manage to represent acceleration? Is the energy equation a mathmatical concept that just fits or is that equation actually what energy is and if so how is it justified?
I think too deeply about the fundamental stuff that the maths eludes me because I fail to make the connections in an intuitive way.
Anyway, made some claims that are likely false but I figure being proved wrong is a great way to learn.

2. Jan 4, 2016

### davenn

why would you think that ?

have you not heard of Newton's first law of motion ?

3. Jan 4, 2016

### A.T.

Nothing in idealized laws of physics matches real world situations exactly. Straight line motion assumes no forces acting (or all forces canceling exactly), which is not the case In the situations you describe. But for many applications the deviations are negligible.

4. Jan 4, 2016

### callmespitfire

I have. But I am not agreeing to it if it is not true.

5. Jan 4, 2016

### callmespitfire

I understand that nothing is exact in terms of mathmatical abstracts not actually being reality but there is a massive mathmatical difference between a straight line and a curved one. The double slit experiment requires straight lines. I'm simply inferring that perhaps particals and objects move in curves and not straightlines because everything in the universe has angular momentum and is moving in a curved path.

6. Jan 4, 2016

### callmespitfire

*double slit expirement disagrees with straight lines

7. Jan 4, 2016

### A.T.

Depends on the amount of curvature

Angular momentum doesn't imply a curved path.

8. Jan 4, 2016

### callmespitfire

I don't really know what it's called but an object moving in an orbit is curving and everything is moving in an orbit. Thus nothing is moving in straight lines unless it'snot orbiting that is. The only thing that I can think of that isn't orbiting is an object falling into the Centre of the universe along it's axis or rotation.

9. Jan 4, 2016

### Staff: Mentor

There is no such thing as the center of the universe.

Imagine you are in deep space, far from any other object (say a light year away from any star). You throw a ball. Can't you see (imagine) it traveling in a straight line?

10. Jan 4, 2016

### DrStupid

The straight lines apply to inertial systems in Euclidean space and in absence of forces.

Conservation of momentum and angular momentum are independent from each other.

11. Jan 4, 2016

### TonyS

callmespitfire, I find your post fascinating, to me it illustrates the difficulty we sometimes have with physics because of the way our mind visualises ideas.
You might want to consider the idea of something moving in a straight line to a sufficient approximation, where 'sufficient' is determined by the nature of the physical problem under consideration. A feel for the relevant orders of magnitude or degrees of precision required in a problem can be a great help here.
Here is the opening paragraph from Landau's course of theoretical physics, volume 1, not about motion in a straight line, but still relevant to your problem, I think;

'One of the fundamental concepts of mechanics is that of a particle. By this we mean a body whose dimensions may be neglected in describing its motion. The possibility of so doing depends, of course, on the conditions of the problem concerned. For example, the planets may be regarded as particles considering their motion about the Sun, but not in considering their rotation about their axes.'

In other words, as a physicist you have to learn to accommodate different levels of approximation in your thinking, depending on the context.
Hope this helps.

12. Jan 4, 2016

### Staff: Mentor

Not really. If you do a series expansion then any line can be approximated as a straight line plus a bunch of other terms. If those other terms are small then the difference between a straight line and a curved line is also small.

Suppose that you have a lab which is 10 m long and a measuring device sensitive to 1 ppm. Then any curve with a radius of curvature greater than 10000000 m will be indistinguishable from a straight line.

So there is not really a massive mathematical difference. A curvature of 0 is just a point on a continuum of curvatures.

13. Jan 4, 2016

### nasu

I think that one point is missing, to clarify the OP.
You seem to have a problem because you expect the object to move in a straight line in any reference frame you can imagine.
You accept that it may move in a straight line on Earth but then you consider Earth's rotation and other motions. This means that you are considering the trajectory in various reference frames and expect to be a straight line in all of them.
This is not what newton's law predicts.
The laws are valid in a specific set of reference frames, the inertial systems.
If we accept that the Earth is a good approximation of an inertial system we can have a body moving along a pretty straight line. The motions of the Earth does not change the shape of the trajectory in respect to the Earth.
But if you switch to another frame, which does not move by just a uniform translation in respect to the Earth, the trajectory may have any other shape. This does not contradict Newton'e laws.

14. Jan 4, 2016

### ehild

Physics is observation and measurements, and their explanation in the frames of some theory. Observation and measurement are connected to reality. The theory is made by our brains, about a model we thought out and that theory is about the model, not about reality. Our observations are limited and measurements have some finite accuracy. We can not describe the real word, but we can make such theories which predict observation and measurement results within their accuracy. With the help of those theories, we can send spacecrafts to the desired planet, we can predict the time of a solar eclipse, we are able to make computers and so on.
Our basic observation is that we live in space and time. Objects move in space, changing positions as time goes on. Human brain created the concept of the dot, the straight line, the circle and so on, and started to play with these concepts and created Geometry. Working with the concept of point mass which changes position with time, the concept of velocity and acceleration were defined. First, people thought that there was something that maintained uniform linear motion. Later on, more accurate observation lead to the conclusion that uniform motion along straight line was the basic behaviour of the bodies, and something was needed to change it, That something was called force, and the theory developed by Newton is called Classical Mechanics. It is not reality. It is about the model where Newton's axioms are valid. That model is good enough in the world we observe around us - see and hear and sense, bodies moving slowly, with speed much less than the speed of light, and an object, far away from other objects to interact with, move along straight lines, as light rays travel from the Sun to our Earth.
More accurate measurements has shown the inaccuracy of Classical Mechanics and more advanced theories arose, which were better, but not enough in the light of more advanced observations. No theory will completely describe the real world. We play with the virtual reality of our model worlds.

15. Jan 5, 2016

### callmespitfire

Isn't both the angular momentum and the momentum conserved though? What makes them different and can they behave in dependant of one an other?
If an astronaut in space lands on the axis of the moon then will he only gain angular momentum or will he gain both angular momentum and normal straight line momentum?
Then if the astronaut using propulsion tries to fly in a straight line we say the coriolis effect will imply that as he moves forward the moon will move from under him so that he would draw a curved path over the surface if his thrusters where to draw a line below him. However he has got angular momentum too as he was spinning to start with so his straight line path cannot be straight if simply pushes forward on his thrusters.
Could it not be that particals behave this way on earth? Not lines but lines with spin?

QUOTE="DrStupid, post: 5334513, member: 352329"]Conservation of momentum and angular momentum are independent from each other.[/QUOTE]
Isn

16. Jan 5, 2016

### callmespitfire

I tend to think about it this way, different people have different views of reality. Between the two is a whole host of probabilities and both might not agree on something, eg, whether two objects that can't be moved are the same height. While they don't agree, reality is split into two possibilities both being unsure. So they pull out a ruler, but one thinks the spaces between the units are uneven so they do a geometry proof that both have to then agree to. They could fight about the axioms all day but they would get nowhere. As developing axioms is better than not developing axioms mathmatical conjecture and absolute proof are born, the model for developing the units is absolutely certain within it's axioms. So they agree that the ruler is as sound as they can both physically make it out to be but never perfect. Once the objects heights are measured they both must agree that they are approximately the same height, the approximation would arise from the imperfect ruler and shaky crafting but if the ruler was perfect then would not the two objects be measured perfectly?
Either way the two realities must then coinside on the approximation.
would I be right in saying that this is the waymathmatics and physics are linked?

17. Jan 5, 2016

### ehild

If I understand you correctly, you are right, You can develop highly accurate measuring tools and create very advanced theories so as the result would correspond to reality more than with a less advanced method. But you can not refine a method to deal with a phenomenon which does not fit to its axioms.
You can not make Classical Mechanics better, so as it can describe the emission spectrum of atoms. For that, Quantum Mechanics had to be invented. Classical Mechanics was not good enough to predict the motion of Mercury accurately enough. For that Relativity Theory was needed. If you apply these theories in common situations, like falling an apple from a tree, you should get the same result as with Classical Mechanics, within the accuracy of the everyday tools to measure distance and time. If you are satisfied with that accuracy, you can use Classical Mechanics, and even more approximation within it. If you want to estimate the height from where the apple fell, by measuring time, you do not need to take the motion of Earth into account.
I suggest to read Leon Lederman's book The God Particle - if the universe is the Answer, What is the Question?

Last edited: Jan 5, 2016