# Can an object be at rest in its own reference frame?

Gold Member
Summary:
Would that violate the uncertainty principle, or is assuming that it would simply a misunderstanding of the UP? (any explanation level welcome)
In classical physics, every object is obviously at rest with itself, and it makes perfect sense for this to be true.

But would this violate the uncertainty principle for a particle? If you are the particle and you know that you're at rest with respect to yourself, you know both your location and your momentum fully.

Or, instead is this idea a misapplication of the uncertainty principle (which I would assume would only apply to measurements we make of a particle, not the person making the measurement, who is at rest with respect to his/her own reference frame)?

Any insight is welcome, at any level.

PeroK
Homework Helper
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What you're really asking is: does the classical view of a particle violate the UP? And the answer is of course it does!

vanhees71 and bhobba
Gold Member
What you're really asking is: does the classical view of a particle violate the UP? And the answer is of course it does!
Thanks. So nothing can be at rest in its own frame?

Or wait, you're saying a PARTICLE can't be at rest in its own frame. I suppose there is a point when an "object" can as it increases in size. (thinking correspondence principle here)

Gold Member
This still seems rather odd to me. Because if I'm a particle, I've already defined my origin as where I'm located. I'm not making a measurement, I'm just existing. Unless no particle has a location or momentum until it is given to them by a measurement. Which renders the whole reference frame thing meaningless, in the same way that light can't have an inertial rest frame.

Yeah, this is definitely weird. I feel like there is a blending between the measureer and thing that is measured, here. Or does measurement not actually have anything to do with it, and a particle simply does not have any particular location or momentum at all on its own?

atyy
Which renders the whole reference frame thing meaningless, in the same way that light can't have an inertial rest frame.

Generally, an inertial reference frame is one in which the laws of physics take a certain form, so we don't need the concept of a particle at rest in order to define an inertial reference frame.

bhobba
Gold Member
Generally, an inertial reference frame is one in which the laws of physics take a certain form, so we don't need the concept of a particle at rest in order to define an inertial reference frame.
But doesn't the idea of an inertial reference frame come automatically with the idea of fixed, definite locations?

A. Neumaier
In classical physics, every object is obviously at rest with itself, and it makes perfect sense for this to be true. But would this violate the uncertainty principle
In classical physics, there is no uncertainty principle. Any classical rigid body has a rest frame, in which it does not move.

But classical physics is not universally applicable and must be replaced by quantum physics in the microscopic domain. There one has the uncertainty principle and no rigid bodies - everything oscillates.

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vanhees71 and bhobba
atyy
But doesn't the idea of an inertial reference frame come automatically with the idea of fixed, definite locations?

In quantum mechanics, the inertial reference frame comes with the idea of fixed classical spacetime. However, it doesn't mean that objects "existing" in the spacetime must have exact positions.

bhobba
Mentor
In quantum mechanics, the inertial reference frame comes with the idea of fixed classical spacetime. However, it doesn't mean that objects "existing" in the spacetime must have exact positions.

Just to expand, in more advanced work an inertial frame is not defined as one in which free particles remain at rest or continue to move at a constant velocity in a straight line. Instead it is defined like much of modern physics in terms of symmetry principles. Specifically its a frame in which the laws of physics are the same at all points of space, at all times, and in all directions. Thus it applies to all areas of physics, not just classical mechanics. Now using a bit of calculus you can show any two inertial frames are moving at constant velocity wrt to each other. The converse however may or may not be true - it turns out to be true - but logically it does not have to be. Newtons first law then becomes - any frame moving at constant velocity to an inertial frame is also inertial. The principle of relativity states an even greater symmetry - the laws of physics are the same in any inertial frame. I will leave it as a advanced question - in General Relativity are the laws of physics the same - Einstein got slightly confused with that one initially - look up Kretchmann - but as I say its an advanced topic that's perhaps even a bit controversial.

Anyway getting back to classical mechanics Landau shows in his famous book - Mechanics - that using the principle of least action all free particles obey the usual first law. But wait - where does the principle of least action come from? QM - it follows easily from the path integral formulation.

Bottom line - everything is really quantum.

Thanks
Bill

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vanhees71