Motion/Rest: Definition & Explanation

[ManishR]

Let say there is just one object 'A' in whole space nothing else! (it means u don't have any other reference system)

What does it mean that the object is in motion or at rest ?

What is motion/rest anyway ?

 

[russ_watters]

Motion is change in position (a displacement) with respect to another object or reference frame in an interval of time.

If there is no other object or reference, an object cannot be said to be in motion - all you can really say is that it is at rest with respect to itself.

 

[LostConjugate]

Well motion and rest is a comparison of two different objects, so it takes more than one. Then motion becomes the energy difference between two objects.

If one object observes another with a higher velocity it would say that object has more energy then itself. Of course the other object would say the same thing of the first object, since it is relative. However when the two objects collide the total energy adds up correctly.

 

[Dr Lots-o'watts]

What about rotation? In this case, the object is moving relative to itself.

Also, a single object accelerating in a field could be said to be moving (as long as you don't ask what's causing the field.)

 

[diazona]

What about rotation? In this case, the object is moving relative to itself.

It's not moving relative to itself, but it is moving relative to whatever reference you use to define a lack of rotation.

If an object were truly the only thing in the universe, it's sort of an open question whether or not it would be able to tell if it's rotating. See Mach's principle on Wikipedia. (Although it's also kind of an unphysical question because there's no way we could ever observe a universe with only one object in it.)

 

[Dr Lots-o'watts]

If the object is separable, it might weaken over time due to the constant outward acceleration, and become more than one object.

 

[ManishR]

Then what does it mean
"speed of an object can never attain c"
what is reference frame in above statement ?

 

[khemist]

The speed can approach c but never attain c.

it is in any reference frame i believe.

 

[LostConjugate]

Hold on hold on, OP says 1 object, you can't rotate one object unless it is made of other objects, which defeats the purpose of the example.

So what OP obviously meant is a point particle.

Furthermore since we are only speaking of motion it is clear we should work in 1 dimension.

 

[LostConjugate]

Then what does it mean
"speed of an object can never attain c"
what is reference frame in above statement ?

ManishR,

A reference frame is a point of view from a specific speed. So for example the point of view from a bystander at a train station is that the train is going very fast along with everyone in it, the point of view from someone in the train is the everyone in the train is at rest while the bystander is going by very fast. These are two different reference frames.

 

[ManishR]

what is rest mass then ?
rest with respect to what ?

 

[ManishR]

by the way what is maximum acceleration possible

 

[LostConjugate]

what is rest mass then ?
rest with respect to what ?

With respect to it's own reference frame.

 

[LostConjugate]

by the way what is maximum acceleration possible

I think it is $$\frac{300,000km}{(tP)^2}$$

In other words you can't go faster than c in the smallest amount of time possible. tP is the Plank Time.

 

[ManishR]

With respect to it's own reference frame.

what does that mean ?

distance between origin of its own reference frame and center of mass always remain constant in time unless its shape or size changes (which is restricted by the definition of object) .

 

[LostConjugate]

what does that mean ?

distance between origin of its own reference frame and center of mass always remain constant in time unless its shape or size changes (which is restricted by the definition of object) .

For example if you were in the same reference frame as light, traveling at the speed of light, then light would appear to have zero mass which is what it's rest mass is.

This is because light would not have any speed from your point of view, therefore no kinetic energy, therefore no mass. Not to say light slows down as you speed up to it's speed, it is the same in all reference frames. But for simplification, you can see how as you speed up to an object's own reference frame it's mass changes from your point of view.

 

[JDługosz]

I think it is $$\frac{300,000km}{(tP)^2}$$

In other words you can't go faster than c in the smallest amount of time possible. tP is the Plank Time.

No, the ramping up of velocity to approach c, while gaining mass, is going on at small time scales. Dumping some amount of kinetic energy into the object would produce some speed 0.999999whatever, no matter how quickly you brought it up to that speed. You don't stop doing SR just because you accelerate hard!

 

[LostConjugate]

No, the ramping up of velocity to approach c, while gaining mass, is going on at small time scales. Dumping some amount of kinetic energy into the object would produce some speed 0.999999whatever, no matter how quickly you brought it up to that speed. You don't stop doing SR just because you accelerate hard!

But since there is a smallest unit of time (dt or tP) whatever you want to call it, there is a limitation on the acceleration.

 

[diazona]

For example if you were in the same reference frame as light, traveling at the speed of light, then light would appear to have zero mass which is what it's rest mass is.

Light does not have a reference frame. It travels at a certain speed, c, in all reference frames.

This is because light would not have any speed from your point of view, therefore no kinetic energy, therefore no mass. Not to say light slows down as you speed up to it's speed, it is the same in all reference frames. But for simplification, you can see how as you speed up to an object's own reference frame it's mass changes from your point of view.

It does work that way for massive objects (not photons). The rest mass of an object is the energy of the object as measured by an observer who perceives the center of mass of the object to be at rest.

 

[diazona]

But since there is a smallest unit of time (dt or tP) whatever you want to call it, there is a limitation on the acceleration.

Actually, you can't really say that the Planck time is a smallest unit of time. It's really just the particular unit of time that can be expressed as a combination of fundamental constants. You could maybe say it's the "preferred" or "natural" unit of time in our universe. I've heard arguments that it may set the limit on the resolution of any physical clock, but it doesn't mean smaller amounts of time don't exist.

Your argument that there's an upper limit on acceleration is interesting, but I'd take it with a few grains of salt, at least without having some references to back it up.

 

[LostConjugate]

Light does not have a reference frame. It travels at a certain speed, c, in all reference frames.

It does work that way for massive objects (not photons). The rest mass of an object is the energy of the object as measured by an observer who perceives the center of mass of the object to be at rest.

Yea I might of went overboard talking about light with zero speed. I just wanted to use the zero rest mass as a good example of how mass, energy and reference are connected.

Actually, you can't really say that the Planck time is a smallest unit of time. It's really just the particular unit of time that can be expressed as a combination of fundamental constants. You could maybe say it's the "preferred" or "natural" unit of time in our universe. I've heard arguments that it may set the limit on the resolution of any physical clock, but it doesn't mean smaller amounts of time don't exist.

Your argument that there's an upper limit on acceleration is interesting, but I'd take it with a few grains of salt, at least without having some references to back it up.

Yea I guess my point is that there is some limit in time we refer to as dt and so there must be some limit to acceleration. It's just another one of those limit paradoxes like how does a man walk across the room to bump into the wall if an infinite number of processes taking a finite amount of time each is required.

The calculus proposed that there is a limit, and we call it dt, but plank units seem to be the new physical dt, dx, etc based off experimentation.

 

[diazona]

Yea I guess my point is that there is some limit in time we refer to as dt and so there must be some limit to acceleration. It's just another one of those limit paradoxes like how does a man walk across the room to bump into the wall if an infinite number of processes taking a finite amount of time each is required.

The calculus proposed that there is a limit, and we call it dt, but plank units seem to be the new physical dt, dx, etc based off experimentation.

No... it sounds like you're misinterpreting the idea of a "limit" in calculus to mean some particular value, which limits how small an increment of time (or whatever) can be. But that's not what it means at all. The dt ("differential time") used in calculus is truly infinitesimal - it's smaller than any finite number, even the Planck time. The idea behind a limit is that, as the time between your measurements gets smaller and smaller, those measurements give you a better and better approximation to the actual thing you're measuring. So whenever you see dt in a mathematical expression, think of it as mathematical notation for "the smaller you make your time intervals, the closer you will get to this result". The dt doesn't represent a real number.

Now, it just happens that the Planck time is a really really short time interval, shorter than any other time people generally like to think about. So if you can theoretically shrink the interval between your measurements to the Planck time, you'll usually have a pretty good approximation. But there's no reason that has to be the case. A different universe with different physical constants could have a very long Planck time, and in that case it would be a pretty lousy approximation. But even in such a universe, calculus would still work, and dt would still be infinitesimally short. It would be patently obvious that dt and the Planck time are completely different and unrelated concepts.

Anyway, the point to take away is that there doesn't necessarily have to be any such thing as a shortest interval of time.

 

[Dr Lots-o'watts]

So what OP obviously meant is a point particle.

In this case, we are quantum and thus talking about spin, no?

In the classical world, rotation is a distinguishable motion, even with a single body. If the body is rigid, I can draw a red dot near the circumference that will be in acceleration relative to the center of rotation, and relativistic effects, for example, can be calculated.

If the body is more realistic, then it is somewhat elastic, so its diameter is a function of rotation speed.

In both cases, the body can emit gravitational waves, and if electrically charged, EM waves (photons), in magnitudes corresponding to rotation speed. But I'll grant that gravitational and electrical fields are ultimately defined from the behavior of at least two distinct objects.

But for a single particle, I think rotational motion is associated with spin. Whether spin is motion or not, I'm not sure. It is angular momentum. Classically, angular momentum is associated to rotational motion, but quantum mechanically, I'm not so sure.

 

[maxverywell]

If the object is alone in whole space that means that there are no any field. So it can moving with constant speed u=0 or non zero. But this two states are equivalent.

 

[brainstorm]

1) any object always emits a certain amount of radiation, however small. So every object is at rest relative to its own EM emissions, even if it would be the only object in the universe, right?

2) if an object was the only one in the universe and it accelerated, this would be evident in inertial resistance to the acceleration, no? Therefore I think the object could be said to be accelerating relative to itself, even if it remains motionless relative to itself - although this is admittedly counterintuitive. I would even compare this with gravitational potential energy, where a stationary object experiences force without moving.

This issue reminds me of Einstein's comparison between force experienced in a moving elevator without windows and gravitational force, which I believe he noted were indistinguishable in terms of the cause of the force. The issue is important, imo, for contextualizing what it would mean for space/location to be truly relative with regards to force interactions.

 

[diazona]

1) any object always emits a certain amount of radiation, however small. So every object is at rest relative to its own EM emissions, even if it would be the only object in the universe, right?

Makes sense, but then again, once you introduce electromagnetism, the object is no longer the only thing in the universe.

2) if an object was the only one in the universe and it accelerated, this would be evident in inertial resistance to the acceleration, no? Therefore I think the object could be said to be accelerating relative to itself

Actually that would be acceleration with respect to an inertial reference frame. The object would be able to "feel" that it was accelerating with respect to an inertial reference frame, but that doesn't mean it's moving/accelerating with respect to itself. Or more precisely: it can "feel" that it is in a noninertial reference frame, but it is still at rest with respect to that noninertial reference frame.

And actually, that is the pre-GR view of the matter. In general relativity, at least according to the Wikipedia article on Mach's principle (which seems to make sense, though I haven't seen the math behind it), the distinction between inertial and non-inertial reference frames arises from the frame-dragging effect from all the other matter in the universe. Without other matter, perhaps all reference frames would be inertial. If that's the case, in a universe that contains only one rigid object, the object would not be able to tell whether it was rotating. Or to think of it another way, there would be no such thing as rotation without other matter to define an inertial reference frame.

 

[brainstorm]

If that's the case, in a universe that contains only one rigid object, the object would not be able to tell whether it was rotating. Or to think of it another way, there would be no such thing as rotation without other matter to define an inertial reference frame.

Good point. But if the object's rotation was accelerating, wouldn't there have to be tension between the constituent particles that make up the object? In fact, even if it was rotating at constant speed, wouldn't the rotation counteract the centripetal force of gravity acting on the particles of the object? I think an earlier post mentioned this by saying that a rotating object could break apart from its momentum.

 

[MarsWTF]

Let say there is just one object 'A' in whole space nothing else! (it means u don't have any other reference system)

What does it mean that the object is in motion or at rest ?

What is motion/rest anyway ?

If you put some energy on this object, i think you may be sure its in motion since.

 

[diazona]

Good point. But if the object's rotation was accelerating, wouldn't there have to be tension between the constituent particles that make up the object? In fact, even if it was rotating at constant speed, wouldn't the rotation counteract the centripetal force of gravity acting on the particles of the object? I think an earlier post mentioned this by saying that a rotating object could break apart from its momentum.

Well, that's kind of the way it works in our universe, with its widespread distribution of matter. Particles naturally "want" to fly off in a straight line, a.k.a. geodesic.* When an object rotates, there is some centripetal force (which could be gravity or electromagnetic etc.) that keeps the particles from doing that, so they move around in circular trajectories. If the rotation is fast enough, the centripetal force might be insufficient to keep the particles in those circular trajectories, and then the object would break apart.

Note the * which means there's a caveat. If I'm interpreting the theory correctly, the only reason that, in our universe, geodesics are straight lines leading out into space, is because those are the trajectories that "follow" the motion of the universe as a whole. But if the rotating object were the only thing in the universe, that argument falls apart. The geodesics, the "natural" trajectories of the particles, are no longer straight lines that extend out into space. Instead, the geodesics would actually be the same circular trajectories that the particles need to be on in order to keep the object rotating, because those are the trajectories that best "follow" the motion of the universe as a whole. So in this case, the particles of the object would stay together simply because that is their "natural" motion, and there would be no need for any centripetal force to keep them together.

Of course, a particle moving along a geodesic is in an inertial reference frame, kind of by definition. So in the last case, with the lone rotating object, each particle would perceive itself to be in an inertial reference frame. Same goes for the object as a whole; it would perceive itself to be in an inertial reference frame, and therefore it would not "realize" that it was rotating at all.

 

[brainstorm]

If you put some energy on this object, i think you may be sure its in motion since.

Ironically, this thread is so abstract because how would you put energy into an object without a source of the energy and an "equal and opposite reaction" in the source? So energy can only really be relative to the interaction that exchanges the energy in the first place, right? But in the object's own frame of reference, it need not behave as if it is in motion if its inertia has stabilized, I think. I.e. Translocation can only be relative where multiple locations are taken into account, right?