Can anything really be at rest?

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IMO, this is disjoint and nonsensical.In summary, the conversation discusses the concept of rest in physics and how it relates to momentum and quantum mechanics. It is argued that nothing can truly be at rest due to the uncertainty principle and the nature of momentum in quantum mechanics. The concept of lambda and its relation to infinity is also discussed. The conversation ends with a question about the possibility of particles constantly accelerating in any inertial reference frame.
  • #1
TheAtheistKing
We set speed v=0 all the time in physics, and reach neat and tidy conclusions, but can anything really be at rest? I am interested in criticisms to the following line of reasoning:

Definition of momentum

[tex] \vec P = mass*velocity = M \vec v [/tex]

And from this it follows that the magnitude of the momentum of a particle is equal to the particle's mass times the particle's speed.

In quantum mechanics the magnitude of the momentum of a particle is equal to Planck's constant divided by the wavelength of the particle.

[tex] |\vec P| = \frac{h}{\lambda} [/tex]

Hence we have:

[tex] m|\vec v| = \frac{h}{\lambda} [/tex]

So if something is at rest, then we have:

[tex] 0 = \frac{h}{\lambda} [/tex]

But nothing can really be infinite, so lambda cannot be infinite, hence the RHS must be nonzero. Hence if the fundamental relation of quantum mechanics is correct, then it follows that nothing can have speed |v|=0, hence no particle can be truly at rest.

Notice I have ignored the center of mass of bodies, but so focus on particles for now. Can any particle truly be at rest? If the above line of reasoning is fine, then wouldn't that mean that in any inertial reference frame whatsover, any particle is accelerating? And if that is the case, would this not explain why there was a second moment in time? And would this not explain why relative motion cannot cease?

Any thoughts?
 
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  • #2
With the uncertainty principle, the product of the uncertainty of position and of momentum is greater than a small constant. So if you had a particle at rest, the uncertainty in its momentum would be zero, and hence the uncertainty of its position would be infinite. It could be anywhere in the universe, and any measurement that told you where would increase the uncertainty of its momentum, leading it to be no longer at rest. So uncertainty agrees with you calculation based on the older quantum mechanics.
 
  • #3
Originally posted by TheAtheistKing
Definition of momentum

[tex] \vec P = mass*velocity = M \vec v [/tex]
No. This is not a true definition of momentum. It is an equation, which is a vicarious mathematical convenience. Momentum, IMO, is better defined in words as: the ability to impart impulse.




Originally posted by TheAtheistKing
In quantum mechanics the magnitude of the momentum of a particle is equal to Planck's constant divided by the wavelength of the particle.

[tex] |\vec P| = \frac{h}{\lambda} [/tex]

Hence we have:

[tex] m|\vec v| = \frac{h}{\lambda} [/tex]
This quote begins with, "In quantum mechanics ...," and has a classical mathematical relationship as a conclusion. IMO, this is disjoint and nonsensical.




Originally posted by TheAtheistKing
But nothing can really be infinite, so lambda cannot be infinite, ...
Why does lambda qualify as "not nothing?" First, define lambda. Then, decide whether or not it should follow this strange rule of not being infinite. I don't understand where you got this rule, or why it should apply to lambda since it has not yet been defined.




Originally posted by TheAtheistKing
... in any inertial reference frame whatsover, any particle is accelerating?
That's a very interesting way to look at it.




Originally posted by TheAtheistKing
And if that is the case, would this not explain why there was a second moment in time?
I don't follow.
 
  • #4


Originally posted by turin
No. This is not a true definition of momentum. It is an equation, which is a vicarious mathematical convenience. Momentum, IMO, is better defined in words as: the ability to impart impulse.

One symbol was defined as the product of two other symbols. If you know the meaning of those two symbols, then you know the meaning of this definition. One symbol is 'v' for velocity, which is adequately defined mathematically, using a three dimensional rectangular coordinate system. Let (x1,y1,z1) be the coordinates of a particle, at some moment in time in some reference frame. The position vector of the particle relative to the origin of the frame is:

R = x1i + y1 j + z1 k

where i,j,k are unit vectors

The velocity of the particle is the derivative of the position vector in this frame with respect to time in this frame.

The other term in the definition is M for mass. It is not immediately clear whether or not M is a function of v. Perhaps the best thing to do would be to provide for M an operational definition, in other words a way of measuring mass. If we assume that inertial and gravitational mass are equivalent, then weighing two bodies in a constant gravitational field would give a method of measuring mass, and hence we would have an operational definition of M. On the other hand, if they are not equivalent then we would have to use collision analysis. But in either case, M can be operationally defined, and the meaning v is clear based upon mathematical work spanning the past 2000 years alone. A particle is too small to have its speed in a frame measured, so no operational definition of v can ever be given.

Momentum then is simply the product of these two variable quantites.

Why criticize such a simple definition? Is impulse a more basic concept of physics than momentum?



This quote begins with, "In quantum mechanics ...," and has a classical mathematical relationship as a conclusion. IMO, this is disjoint and nonsensical.

Planck's constant divided by wavelength has the same units of the P that was defined, so perhaps they are equivalent. Even if they aren't equivalent, so long as they are proportional, an arbitrary constant will not affect the conclusion we are seeing here. The question then is, are they proportional?


Why does lambda qualify as "not nothing?" First, define lambda. Then, decide whether or not it should follow this strange rule of not being infinite. I don't understand where you got this rule, or why it should apply to lambda since it has not yet been defined.

Why can't lambda be left undefined? What is an operational definition of lambda? Why does the concept that no quantity of physics is infinite qualify as strange?

I don't follow.

Here I think the guy is just seeing the obvious. If nothing can truly be at rest in an inertial frame, then in no inertial reference frame can anything be moving at a constant speed. Hence, at the beginning of time, every particle which was somewhere was simultaneously subjected to a nonzero force, which would mean that in any inertial reference frame the particles were being observed from, those particles would move relative to one another, providing a second state.
 
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  • #5
I was merely appealing to the wishes of TheAtheistKing:
Originally posted by TheAtheistKing
I am interested in criticisms to the following line of reasoning:
...
Any thoughts?
 
  • #6


Originally posted by Tempest
Originally posted by turin One symbol was defined as the product of two other symbols.
...
Why criticize such a simple definition? Is impulse a more basic concept of physics than momentum?
Correction: "one physical quantity was equated to the product of two other physical quantities. I don't appreciate the patronization. It is quite obvious to me, as I'm sure to anyone who reads the post, what those "symbols" are intended to represent. That was not the issue I wanted to address. The issue at hand is whether this particular equation is suitable as a definition. It may seem like I am arguing semantics, and in a way I am and appologize. But in this case it is a nontrivial distinction. Momentum is just not generally defined by this equation, period, plane and simple, whether or not my definition is appropriate by the standards of more accomplished and rigorous physicists. If you want to use the term "momentum" and define it with this equation, then we don't really have anything more to say to each other about it.




Originally posted by Tempest
Planck's constant divided by wavelength has the same units of the P that was defined, so perhaps they are equivalent. Even if they aren't equivalent, so long as they are proportional, an arbitrary constant will not affect the conclusion we are seeing here. The question then is, are they proportional?
Agreement of units is hardly a condition on which to base an identity. So the units agree, that doesn't really tell you anything positive. Agreement of units is one of the many considerations in determining whether or not a relationship is legitimate.




Originally posted by Tempest
Why can't lambda be left undefined? What is an operational definition of lambda?
It can be. But my point was exactly that: so far I don't see any operational definition or physical significance for lambda whatsoever in TheAtheistKing's treatment. If I'm playing basketball, I sure hope that I don't have to adhere to the rules of soccer; it would be awefully difficult to play the game without using my hands. Until lambda is defined, at least in some way, how could rules be imposed on it? I can say this: if lambda has the same meaning to which I am accustomed, then this relationship between the QM and CM momenta should not be taken so seriously as to make such a profound claim.




Originally posted by Tempest
Why does the concept that no quantity of physics is infinite qualify as strange?
It is not a strange requirement for physical, or should I say, tangible quantities, but so far I don't see how lambda fits into this category of quantities.




Originally posted by Tempest
Here I think the guy is just seeing the obvious.
Well, it may be obvious to geniuses like yourself, but I was hoping to hear some feedback from the author. I would like TheAtheistKing to elaborate on what was meant.
 
  • #7
wow i think there is too much thinking going on here...The question was, can anything ever have zero (none, null, 0) velocity movment positional change...the answer is sure, provided you meet this one small thing...Figure out a way to stop the millions of millions of trillions of strings that are vibrating in that object...Thats all there's too it...He didn;t ask how to do it he just asked if it could be done...How to do it would be a far better and more fun question don't you think? :smile:
 
  • #8
I think the Atheist King's whole point is that you shouldn't be too sure. Here we see a quantum mechanical argument which results in the conclusion that no particle can be at rest. He didn't say that the center of mass of a body couldn't be at rest. As for strings, they are theoretical entities, as are point particles. One has a zero dimensional object as the fundamental unit of matter, the other has a one dimensional object as the fundamental unit of matter. Both units are theoretical.

And he made a very interesting observation, which is that if the momentum of a particle really is given by Planck's constant divided by the wavelength of the particle, then every particle is accelerating in any inertial reference frame, which would literally be why there was a second moment in time. I am still thinking about this thread.

If you think about it, if all the particles in the universe were free at the first moment in time, then the law of inertia would rule each and every particle. Nothing would move. On the other hand, if there were forces between every particle, then each particle would accelerate, and thus they would move relative to each other. So what he is clearly saying is this:

Granted that the quantum mechanical relation for momentum of a particle is correct, it follows that there are no such things as free particles in nature. Thus, all particles are 'connected' somehow, exerting forces between each other. This should remind you of gravity. If every particle in the universe gravitationally attracts every other particle, then no particle is ever force free, which is his main conclusion.
 
  • #9
No. Being in a state of perfect rest would mean being at temperatures of absolute zero, which is made impossible by the thermodynamics.


You cannot win- you can not get something for nothing because matter and energy are conserved.

You cannot break even- you cannot return to the same energy state, because entropy always increases.

You cannot get out of the game- because absolute zero is unattainable.

Dr. Michio Kaku, Hyperspace
 
  • #10
Does anyone know how to construct a mathematical argument using thermodynamics, which results in the conclusion that relative motion cannot cease. I'd be interested in looking at it.

Thanks
 
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  • #11
Food for thought on ideal physical situations!

TheAtheistKing, I think this is closely related to your thread! If you don't feel that way, I apologize. I think they are fundamental questions which everyone should be able to answer: however, I am apparently a certified crackpot.

How many of these statements are true?

1.) An ideal clock measures time! That is, the admonishment "only if it is at rest in the frame of reference being used" is a superfluous constraint on the truth of the statement.

2.) The concept of an "ideal clock at rest" does not violate any concepts of Quantum Mechanics!

3,) The reading on an ideal clock in motion is not a direct measure of the change in proper time along its space-time trajectory.

4.) Time and proper time are exactly the same thing!

5.) Only a crackpot would ask such nonsensical questions.

Have fun -- Dick
 
  • #12
Originally posted by Tempest
And he made a very interesting observation, which is that if the momentum of a particle really is given by Planck's constant divided by the wavelength of the particle, then every particle is accelerating in any inertial reference frame, which would literally be why there was a second moment in time. I am still thinking about this thread.
Wavelength is inverse of frequency. Corresponding to infinite wavelength would be frequency of 0. Why would it be unthinkable to consider frequency of 0?
Seems like particle with zero momentum equivalently does not exist.
Makes me think of vacuum..
 
  • #13
I believe you can be at rest.

Consider an inertial reference frame attached to an electron. Anything in this frame is at rest relative to the electron.

Concerning the second question as to the logic of the momentum derivation. I agree that if we think of momentum as force times the time the force is applied, or as the author said impulse, we come to a better understanding. Force and momentum are related through a derivative. Force is the measure of how momentum changes with time. According to the photoelectric effect and common experience (sun bathing for instance) we know light carries energy and therefore exerts a force. The problem arises when we associate momentum strickly with mass. The equation p=mv is, in my opinion, a special case of momentum and not a complete definition.
 
  • #14


Originally posted by tenzin
Consider an inertial reference frame attached to an electron. Anything in this frame is at rest relative to the electron.
Why would you be sure about that? While sitting on my chair I'm following geodesics of spacetime that I perceive as gravity force. What keeps electron together? If it even is "together".

we know light carries energy and therefore exerts a force. The problem arises when we associate momentum strickly with mass. The equation p=mv is, in my opinion, a special case of momentum and not a complete definition.
It falls through to meaning of mass. Light carries mass too.
 
  • #15


Originally posted by wimms
Why would you be sure about that? While sitting on my chair I'm following geodesics of spacetime that I perceive as gravity force. What keeps electron together? If it even is "together".

You are off the topic. A reference frame can be attached to the electron. This is done all the time in relativity.

It falls through to meaning of mass. Light carries mass too.

Mass and energy are related by the speed of light. Since light is pure energy it can have momentum but no mass. It all depends on our concept of mass and its relation to energy. All the original poster is doing is manipulating equations without a knowledge of their meaning.
 
  • #16


Originally posted by tenzin
Consider an inertial reference frame attached to an electron. Anything in this frame is at rest relative to the electron.

If you go back and look at the original poster's argument, he concluded that in any inertial reference frame, a particle must be accelerating. That being the case, any coordinate system which is attached to an electron does not represent an inertial reference frame (because the electron is changing speeds in any inertial reference frame). But, as was said, that conclusion is contingent upon the following equation being true:

[tex] m|\vec v| = \frac{h}{\lambda} [/tex]
 
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  • #17


Originally posted by StarThrower
If you go back and look at the original poster's argument, he concluded that in any inertial reference frame, a particle must be accelerating. That being the case, any coordinate system which is attached to an electron does not represent an inertial reference frame (because the electron is changing speeds in any inertial reference frame). But, as was said, that conclusion is contingent upon the following equation being true:

[tex] m|\vec v| = \frac{h}{\lambda} [/tex]

An inertial reference frame is defined as a coordinate system where a point mass can only move in a straight line with constant velocity. So any frame a particle is accelerating in is not inertial.
 

1. Can an object be completely at rest?

No, according to Newton's first law of motion, also known as the law of inertia, an object will remain at rest unless acted upon by an external force. This means that there will always be some force acting on an object, even if it appears to be at rest.

2. Is there such thing as absolute rest?

No, according to Einstein's theory of relativity, there is no such thing as absolute rest. The concept of rest can only be defined in relation to other objects or frames of reference.

3. How does the concept of rest relate to motion?

Rest and motion are relative concepts. An object that is at rest in one frame of reference may appear to be in motion in another frame of reference. This is known as the principle of relativity.

4. Can energy be at rest?

No, energy is always in a state of motion. In fact, energy is defined as the ability to do work, which requires movement or motion. Even in the absence of external forces, particles at the atomic level are constantly in motion due to their thermal energy.

5. What are some examples of objects at rest?

Objects that appear to be at rest may still have internal motion, such as a stationary car with its engine running or a book sitting on a table with molecules vibrating within it. However, in a truly inertial reference frame, an object at rest would have no external forces acting on it, such as a book sitting on a shelf or a table standing on the ground.

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