# Can anything really be at rest?

1. Dec 16, 2003

### 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

$$\vec P = mass*velocity = M \vec v$$

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.

$$|\vec P| = \frac{h}{\lambda}$$

Hence we have:

$$m|\vec v| = \frac{h}{\lambda}$$

So if something is at rest, then we have:

$$0 = \frac{h}{\lambda}$$

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?

Last edited by a moderator: Dec 16, 2003
2. Dec 16, 2003

Staff Emeritus
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. Dec 16, 2003

### 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.

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

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.

That's a very interesting way to look at it.

I don't follow.

4. Dec 17, 2003

### Tempest

Re: Re: Can anything really be at rest?

Last edited by a moderator: Dec 17, 2003
5. Dec 17, 2003

### turin

I was merely appealing to the wishes of TheAtheistKing:

6. Dec 17, 2003

### turin

Re: Re: Re: Can anything really be at rest?

7. Dec 17, 2003

### Coughlan

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 theres 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?

8. Dec 18, 2003

### Tempest

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. Dec 20, 2003

### caumaan

No. Being in a state of perfect rest would mean being at temperatures of absolute zero, which is made impossible by the thermodynamics.

10. Dec 21, 2003

### StarThrower

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

Last edited: Dec 21, 2003
11. Dec 23, 2003

### Doctordick

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. Jan 2, 2004

### wimms

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. Jan 4, 2004

### tenzin

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. Jan 4, 2004

### wimms

Re: I believe you can be at rest.

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".

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

15. Jan 4, 2004

### tenzin

Re: Re: I believe you can be at rest.

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

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. Jan 6, 2004

### StarThrower

Re: I believe you can be at rest.

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:

$$m|\vec v| = \frac{h}{\lambda}$$

Last edited: Jan 6, 2004
17. Jan 6, 2004

### tenzin

Re: Re: I believe you can be at rest.

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.