A very strange universe indeed!

I don't know whether this has been mentioned yet, but since Newton's second law states acceleration requires a force, therefore circular motion requires a force to be applied and this makes it detectable. Uniform linear motion requires no resultant force and therefore remains undetectable.

sinan90 said:

I don't know whether this has been mentioned yet, but since Newton's second law states acceleration requires a force, therefore circular motion requires a force to be applied and this makes it detectable. Uniform linear motion requires no resultant force and therefore remains undetectable.

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The OP is essentially asking why Newton's laws should be true of the universe, rather than some other set of laws.

Perhaps laws making circular motion natural and requiring a force to travel in a straight line.

It could all boil down to the anthropic principle then. If the laws were different then perhaps we wouldn't be here to "see" them.

In the case of linear motion every part of the body is subject to the same force but in a spinning object there is more force on the outer parts than the inner parts. We sense the differential?

"I don't know whether this has been mentioned yet, but since Newton's second law states acceleration requires a force, therefore circular motion requires a force to be applied and this makes it detectable. Uniform linear motion requires no resultant force and therefore remains undetectable."

Consider that a person accelerating around the earth in orbit feels weightless.<G>

ArnautDaniel said:

The phrase in my post:

"confine its motion to a plane to which the field is normal"

requires that the velocity parallel to the field be zero.

...

You are an experimentalist, aren't you?

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Sorry for not responding to this earlier. No, I'm a theorist. And yes, I see that you said that, but again that's an extreme special case. It's not just a preferred direction, but also specifically confining the motion to a plane. Linear motion is more natural because it doesn't require these extra criteria to happen.

Chalnoth said:

Sorry for not responding to this earlier. No, I'm a theorist. And yes, I see that you said that, but again that's an extreme special case. It's not just a preferred direction, but also specifically confining the motion to a plane. Linear motion is more natural because it doesn't require these extra criteria to happen.

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No, it is only more natural given that we have the physical laws which we have, and not a different set of physical laws.

The real question is why do we have the physical laws we have?

I can generalize the kind of model I gave to a three dimensional space (if you like) and get non-linear motion to be preferred:

1. We'll assign a smoothly varying vector field to every point in space
2. We'll assign every object a mass which may be any real number (positive or negative)
3. We'll make it so our equations of motion are such that the absolute value of the mass acts like the conventional mass, and the value of the mass acts like the charge and the vector field acts locally like a "magnetic field", and use your basic equations of motion for a charge particle in a magnetic field.

Of course the vector field here shouldn't be understood as a magnetic field, it is just a property of space which effects the motion, nothing more. (this is just a model after all)

There we go, natural motion isn't linear except in special cases.

No special critera, just a weird property of space that effects the motion.

Why our space and not a space like this?

99% of all species that ever lived are now EXTINCT is that really INTELLIGENT DESIGN?

It is if you're alive to read the sign.

ArnautDaniel said:

No, it is only more natural given that we have the physical laws which we have, and not a different set of physical laws.

The real question is why do we have the physical laws we have?

I can generalize the kind of model I gave to a three dimensional space (if you like) and get non-linear motion to be preferred:

1. We'll assign a smoothly varying vector field to every point in space
2. We'll assign every object a mass which may be any real number (positive or negative)
3. We'll make it so our equations of motion are such that the absolute value of the mass acts like the conventional mass, and the value of the mass acts like the charge and the vector field acts locally like a "magnetic field", and use your basic equations of motion for a charge particle in a magnetic field.

Of course the vector field here shouldn't be understood as a magnetic field, it is just a property of space which effects the motion, nothing more. (this is just a model after all)

There we go, natural motion isn't linear except in special cases.

No special critera, just a weird property of space that effects the motion.

Why our space and not a space like this?

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Because when you have a space that is defined by that many criteria, there are vastly, vastly more ways for things to be than for them to move in circles. Linear motion requires fewer criteria, and is therefore more natural motion. It's not really a mystery, then, why linear motion happens. There are other things about our universe that are mysterious, but this is not one of them.

Ummm..... folks. This question is not that deep. Think about it.

Rotary motion involves a continually changing velocity vector. The reason it is detectable is that there is a delta V present anywhere in the circular room in question (except on the exact axis of rotation if you want to get particular.)

To put it another way, in example a, there is no change in velocity. The movement is undetectable.

However in example b, take the woman's hand. the velocity chages as the room rotates.

A CHANGE OF DIRECTION IS A CHANGE OF VELOCITY. If it were not so, your tires would not squeal as you took a corner too fast.

AMOG said:

Ummm..... folks. This question is not that deep. Think about it.

Rotary motion involves a continually changing velocity vector. The reason it is detectable is that there is a delta V present anywhere in the circular room in question (except on the exact axis of rotation if you want to get particular.)

To put it another way, in example a, there is no change in velocity. The movement is undetectable.

However in example b, take the woman's hand. the velocity chages as the room rotates.

A CHANGE OF DIRECTION IS A CHANGE OF VELOCITY. If it were not so, your tires would not squeal as you took a corner too fast.

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Yeah, but the criticism that this line of argument assumes the conclusion first is valid. Better to look at where these laws of motion come from in the first place, which is from spatial symmetries. It requires many more special criteria to get circular motion than it does to get linear motion, so linear motion is the more natural. It's as simple as that.

The OP makes a valid point. Mach (and Einstein) spent a lot of time trying to make acceleration operate on the same level as velocities, i.e. it should be a relational property, not absolute.

To some extent Einstein succeeded, but certainly not in the way he would have envisioned.

There's a decent introduction at Wikipedia.

Chalnoth said:

Because when you have a space that is defined by that many criteria, there are vastly, vastly more ways for things to be than for them to move in circles. Linear motion requires fewer criteria, and is therefore more natural motion. It's not really a mystery, then, why linear motion happens. There are other things about our universe that are mysterious, but this is not one of them.

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Well, "simplicity" is a kind of hand wavy notion to begin with.

I mean what makes something simpler than another? What criteria?

Depending on the criteria different things seem simpler.

I recall when I started learning relativistic mechanics it just seemed so much more complicated, whereas Newtonian mechanics seemed so much simpler.

Of course relativistic mechanics is simpler when you use the right criteria for "simplicity", and you find those criteria are much broader than the ones which seemed to indicate that Newtonian mechanics was simpler.

It doesn't strike me as obvious that there might not be a universe out there which has a very broad set of criteria that makes nonlinear motion more natural.

Sure in my model I introduced a weird property of space, but it doesn't strike me as obvious that in some very large and encompassing theory, this sort of space wouldn't exist as a sort of weird complexity that makes the overall theory simpler (much the way that the odder Lorenz transformations make a larger simpler theory than the Galilean transformations could have).

ArnautDaniel said:

Well, "simplicity" is a kind of hand wavy notion to begin with.

I mean what makes something simpler than another? What criteria?

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Fewer parameters makes for a pretty good definition. For example, space without a preferred direction is simpler than space with a preferred direction because defining the direction requires two parameters.

ArnautDaniel said:

Sure in my model I introduced a weird property of space, but it doesn't strike me as obvious that in some very large and encompassing theory, this sort of space wouldn't exist as a sort of weird complexity that makes the overall theory simpler (much the way that the odder Lorenz transformations make a larger simpler theory than the Galilean transformations could have).

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Sounds manifestly unlikely to me. At the very least, for example, you'll have the relationship between the particles' velocities and the radii of their motions, so that's one parameter that doesn't exist in space where linear motion is normal (for example, if a magnetic field picks out the non-linear motion, then the magnitude of the magnetic field is the extra parameter that determines the relationship between radius and velocity).

Chalnoth said:

Fewer parameters makes for a pretty good definition. For example, space without a preferred direction is simpler than space with a preferred direction because defining the direction requires two parameters.

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Yeah, but it could turn out that a theory with a preferred direction in space is simpler in a larger sense (maybe the equations of motion or the action turn out to have a very very nice property, or the preferred direction allows for the elimination of several parameters elsewhere).

Sounds manifestly unlikely to me. At the very least, for example, you'll have the relationship between the particles' velocities and the radii of their motions, so that's one parameter that doesn't exist in space where linear motion is normal (for example, if a magnetic field picks out the non-linear motion, then the magnitude of the magnetic field is the extra parameter that determines the relationship between radius and velocity).

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It might be unlikely, but let us bear in mind contemporary directions in research in particle physics, namely string theories.

By the time you've defined your action on some unlikely and complicated manifold in whatever number of dimensions, it seems pretty evident that whatever motion you would have would be unlikely to be linear on a sufficiently microscopic scale.

You run into the same problems even if it's part of a larger framework, though. The basic issue is that you get from the more fundamental theory (like string theory) to the low energy physics by symmetry breaking. To get things like preferred directions you need more symmetry breaking than for simpler situations. Each additional symmetry breaking is an example of added complexity.

And, of course, yes, you don't expect linear motion to be natural over an infinite region. The relevant point here is that in General Relativity, every region of space-time locally looks flat. That is, if you zoom in on any space-time far enough, no matter how convoluted and ugly, straight motion becomes natural. It's only when you've zoomed out far enough that the curvature of space-time becomes of interest that paths start looking curved, and how far depends upon the nature of the space-time in that region. You'd have to entirely get away from this idea of space-time always looking locally flat to have a situation where circular motion could be considered "natural".