Struggling to understand why uniform motion is so different from non-u

[Seminole Boy]

If all motion is relative, then why is the general theory of relativity so much more dense with mathematics? I'm not asking you to explain the math--there is no way I would ever grasp that. What I'm confused on is why non-uniform motion (accelerated or decelerated motion) is so different from uniform motion. There seems to be some serious physical (mechanical) implications at work here that I'm not understanding.

Here's another way of looking at my question: What does it really mean, physically speaking, to be in uniform motion?

Let's also refer to Einstein's book here. He uses a train and an embankment and a passenger to illustrate this. Conductor hits the brakes and the passenger "jerks" forward. Quote: "The retarded motion is manifested in the mechanical behavior of bodies relative to the person in the carriage." What is he really saying here? Another quote: "...it would appear to be impossible that the same mechanical laws hold relatively to the non-uniformly moving carriage, as hold with reference to the carriage when at rest or in uniform motion."

That last quote is what is really confusing me. Obviously, he goes on to prove that the "it would appear" part is wrong, but WHY is it that inuitively we would think that the laws wouldn't apply to this different form of motion? That's the part I'm missing.

One of other way of explaining my struggle with this: what is so special about acceleration? What am I missing?

Mentz, I like your example. I'm hoping Mr. Donis will show up and clarify it just a little more, or give another example like that one.

 

[1977ub]

As a child, the Nobel Prize-winning physicist Richard Feynman asked his father why a ball in his toy wagon moved backward whenever he pulled the wagon forward. His father said that the answer lay in the tendency of moving things to keep moving, and of stationary things to stay put. "This tendency is called inertia," said Feynman senior. Then, with uncommon wisdom, he added: "But nobody knows why it is true."

That's more than even most physicists would say. To them, inertia does not need explaining, it simply "is." But since the concept was first coined by Galileo in the 17th century, some scientists have wondered if, perhaps, inertia is not intrinsic to matter at all, but is somehow acquired. Those who have tried to come to grips with inertia include Feynman junior, once he had grown up, and Albert Einstein, who tried — and failed — to show that inertia was related to the arrangement of matter in the universe.

- http://www.calphysics.org/haisch/science.html

 

[Mentz114]

Here's another way of looking at my question: What does it really mean, physically speaking, to be in uniform motion?

If you hold a ball in your hand and release it while keeping your hand still

1. If you are in unform motion the ball stays where it is released
2. Otherwise it moves after release, ie experiences an acceleration.

Use your imagination and do some thought experiments.

 

[Seminole Boy]

I like that article, 1977. Good read.

 

[Passionflower]

If you hold a ball in your hand and release it while keeping your hand still

1. If you are in unform motion the ball stays where it is released
2. Otherwise it moves after release, ie experiences an acceleration

For 2 I would prefer:

2. Otherwise it moves after release, you accelerate away from the ball.

 

[WannabeNewton]

If all motion is relative, then why is the general theory of relativity so much more dense with mathematics?

I'm not even seeing the logical conclusion here. What does uniform motion being relative have to do with how mathematical a theory is? To properly formulate Newtonian mechanics for even holonomic systems you need a slew of mathematics that could easily match that of GR if not exceed it. Yet, the physics is unchanged - it is still Newtonian mechanics. So again, how does your question even find logical footing?

 

[rbj]

uniform, unaccelerated motion is equivalent to being stationary, not moving at all.

 

[Seminole Boy]

Wannabe:

Perhaps I shouldn't have put it that way, but obviously the mathematics of general relativity are much scarier than the mathematics of special relativity? So, to me, this has to be connected with the transition from IRF to NIRF.

 

[Mentz114]

Wannabe:

Perhaps I shouldn't have put it that way, but obviously the mathematics of general relativity are much scarier than the mathematics of special relativity? So, to me, this has to be connected with the transition from IRF to NIRF.

It's not that simple. It's the curvature that makes it more complicated. You can have non-inertial states in SR.

 

[1977ub]

Wannabe:

Perhaps I shouldn't have put it that way, but obviously the mathematics of general relativity are much scarier than the mathematics of special relativity? So, to me, this has to be connected with the transition from IRF to NIRF.

Also, GR doesn't make this issue go away. There is still the difference between inertial and non-inertial coordinates, which remains at root a matter of measurement rather than being fully explained.

 

[ghwellsjr]

If all motion is relative, then why is the general theory of relativity so much more dense with mathematics? I'm not asking you to explain the math--there is no way I would ever grasp that. What I'm confused on is why non-uniform motion (accelerated or decelerated motion) is so different from uniform motion.

Perhaps I shouldn't have put it that way, but obviously the mathematics of general relativity are much scarier than the mathematics of special relativity? So, to me, this has to be connected with the transition from IRF to NIRF.

No, you don't need GR to handle a Non-IRF. The problem, if we want to call it a problem, is that although there is a standard way to handle IRF's in SR, there is no standard way to handle NIRF's in SR. But that doesn't mean it can't be done. There's lots of ways to do it. And at least one of those ways does not require math any more complicated than the math used for IRF's.

 

[soothsayer]

Some misconceptions that the OP has, I think:

1) There is no preferred reference for uniform velocity. No constant, uniform motion is truly indiscernible from one another, including v = 0. HOWEVER, there does seem to be a preferred acceleration frame, which is to say that one can conclusively determine a = 0 even in SR. This bothered Einstein greatly, at first, but he was able to come to terms with it. An object with acceleration velocity will have the same nonzero acceleration in any inertial reference frame. In short, acceleration need not be relative to anything.

2) SR can certainly handle acceleration. This is a common misconception. GR is a theory of gravity incorporated into relativity.

3) GR is not as different from Newtonian mechanics and SR, mathematically, as you believe. It LOOKS a lot more complicated, but it is essentially SR in non-Euclidean geometries. That's all. Describing motion in these Riemannian geometries certainly takes more steps, but is not such a jarring departure from SR. So, SR can handle acceleration in Euclidean geometries, but uniform motion in non-Euclidean geometries is really the realm of GR. And actually, on a local scale, the two cases are indistinguishable, but GR has global features that can't be transformed away, unlike SR.

 

[robphy]

If all motion is relative, then why is the general theory of relativity so much more dense with mathematics? I'm not asking you to explain the math--there is no way I would ever grasp that. What I'm confused on is why non-uniform motion (accelerated or decelerated motion) is so different from uniform motion.

It seems the issue of mathematical complexity is similar to the complexity of dealing with accelerated motion vs uniform motion in intro physics 101.

With uniform motion, the equations are simple linear equations.
With constant acceleration, the equations need quadratic equations (possibly motivated by calculus or difference equations).
With general non-uniform motion, you must use calculus.
These can be further complicated by working in various frames of reference.

In my opinion, the simplicity of the uniform motion case is due to the abundance of symmetry.

The mathematical machinery needed for the non-uniform case is still there in the uniform case, if one needs it. But often, symmetry will simplify things (by hiding the machinery).

Here's another way of looking at my question: What does it really mean, physically speaking, to be in uniform motion?

Let's also refer to Einstein's book here. He uses a train and an embankment and a passenger to illustrate this. Conductor hits the brakes and the passenger "jerks" forward. Quote: "The retarded motion is manifested in the mechanical behavior of bodies relative to the person in the carriage." What is he really saying here? Another quote: "...it would appear to be impossible that the same mechanical laws hold relatively to the non-uniformly moving carriage, as hold with reference to the carriage when at rest or in uniform motion."

That last quote is what is really confusing me. Obviously, he goes on to prove that the "it would appear" part is wrong, but WHY is it that inuitively we would think that the laws wouldn't apply to this different form of motion? That's the part I'm missing.

One of other way of explaining my struggle with this: what is so special about acceleration? What am I missing?

(This was copied from a reply I gave in another thread in Classical Physics on rotation.)
The classic "Frames of Reference" video by Hume and Ivey (1960) may be helpful:
http://archive.org/details/frames_of_reference
Non-inertial reference frames are discussed near the 16min mark.
Rotating frames are near the 17min mark.

 

[1977ub]

It seems the issue of mathematical complexity is similar to the complexity of dealing with accelerated motion vs uniform motion in intro physics 101.

With uniform motion, the equations are simple linear equations.
With constant acceleration, the equations need quadratic equations (possibly motivated by calculus or difference equations).
With general non-uniform motion, you must use calculus.
These can be further complicated by working in various frames of reference.

In my opinion, the simplicity of the uniform motion case is due to the abundance of symmetry.

The mathematical machinery needed for the non-uniform case is still there in the uniform case, if one needs it. But often, symmetry will simplify things (by hiding the machinery).

This however doesn't really address why in my coordinates you are accelerating and in your coordinates I am, and yet we can't both be experiencing inertial frame in SR, right? [or more to the point, how to determine which of us experiences inertial frame without making a measurement]

 

[PAllen]

This however doesn't really address why in my coordinates you are accelerating and in your coordinates I am, and yet we can't both be experiencing inertial frame in SR, right? [or more to the point, how to determine which of us experiences inertial frame without making a measurement]

Measurement is the difference. Forget coordinates, the difference is between inertial and non-inertial motion; this difference is based on observation. Coordinates are just inventions of the mind to describe a physical situation.

 

[1977ub]

Measurement is the difference. Forget coordinates, the difference is between inertial and non-inertial motion; this difference is based on observation. Coordinates are ust inventions of the mind to describe a physical situation.

I think where people can get turned around in the beginning is with the realization that unaccelerated motion is relative, i.e. simply a matter of coordinates based on you. No measurement other than the erection of coordinates is required. As you say, this no longer works when acceleration is introduced.

 

[Dale]

If all motion is relative, then why is the general theory of relativity so much more dense with mathematics? I'm not asking you to explain the math--there is no way I would ever grasp that. What I'm confused on is why non-uniform motion (accelerated or decelerated motion) is so different from uniform motion.

The complicated math in GR is not due to non uniform motion. It is due to gravity. You can use tensors and related math in SR.

 

[PAllen]

I think where people can get turned around in the beginning is with the realization that unaccelerated motion is relative, i.e. simply a matter of coordinates based on you. No measurement other than the erection of coordinates is required. As you say, this no longer works when acceleration is introduced.

Coordinates are not measurements. You can erect coordinates 'based on you' using some conventions and many measurements no matter what your state of motion. If you describe laws of motion in coordinates you would set up, and you are moving inertially , the laws will take a particularly simple form - because the law of inertia holds within and inertially moving lab. Within a non-inertially moving lab, the law of inertia does not hold (let go of a ball and it accelerates), and laws will take a more complex form. But as Mentz said many posts ago, the difference is physical: in a lab, let go of a neutral object. If it stays put, your lab is inertial, in GR sense; if ball does not stay put, your lab is not moving inertially, in GR sense.

 

[1977ub]

I was thinking about how inertia is not observed to be *capricious* - even though we don't fundamentally know what it is or where it comes from, and must measure it, it is not observed to just "happen" where it is not expected. For instance, in flat space-time, nothing is observed to simply accelerate without a cause. If you experience being at rest, and someone else who experiences being at rest is accelerating with regard to you, then they must be in warped space-time from gravity... or is there something else? Can large-scale cosmology cause this as well?

 

[PAllen]

I was thinking about how inertia is not observed to be *capricious* - even though we don't fundamentally know what it is or where it comes from, and must measure it, it is not observed to just "happen" where it is not expected. For instance, in flat space-time, nothing is observed to simply accelerate without a cause. If you experience being at rest, and someone else who experiences being at rest is accelerating with regard to you, then they must be in warped space-time from gravity... or is there something else? Can large-scale cosmology cause this as well?

Large scale cosmology can cause this as well. However, the point you raise is a really good one: the physical manifestation of gravity is geometry is that: two free fall bodies having their relative motion change, even though both are inertial, implies there is spacetime curvature = gravity. Large scale cosmology involves spacetime curvature