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I only have limited knowledge of relativity and quantumphysics but as far as I know, the uncertainty principle relates the uncertainty of space and momentum of a particle. Einstein however, explained that space and time are tied together and the real fabric of the universe is spacetime through which all objects navigate.

It feels as if space uncertainty should therefore be spacetime uncertainty. Is this wrong? Can it be that you know the position of a particle but not the exact time when it was there, and that that gives rise to uncertainty in momentum? If so, wouldn't this be a more elegant way to express the uncertainty principle?

Googling for "spacetime uncertainty" gives papers that go far over my head. While my math is good, we barely touched on quantum mechanics in physics.

Qmechanic
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camel
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3 Answers3

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the uncertainty principle relates the uncertainty of space and momentum of a particle.

It is one of the basic foundation stones of quantum mechanics, tied up with the solutions of quantum mechanical equations. Quantum mechanics is a successful theory describing the behavior in the microcosm of particles.

The Heisenberg Uncertainty Principle , HUP, is described mathematically by the commutation relations of quantum mechanical operators operating on the solutions that describe the position and momentum of a particle. In general it concerns pairs of observables and there are a number of pairs that display a HUP uncertainty, not just momentum and position.

Einstein however, explained that space and time are tied together and the real fabric of the universe is spacetime through which all objects navigate.

You are describing General Relativity. This is a classical theory applying to large dimensions in space and time. It is not quantized. The quantization of gravity is an ongoing research subject.

The HUP relations will exist in the appropriate format of the quantized General Relativity observables, once there is agreement on the quantization of gravity.

It has no meaning to mix up the two systems otherwise.

anna v
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  • The idea of a four dimensional spacetime is sufficient for my question, it need not be curved. This flat spacetime is the realm of special relativity which suposedly plays along quite nicely with quantum mechanics.

    I suppose the question boils down to asking if it's consistent to see a particle as a "cloud" of possible situations in spacetime and this uncertainty of where it used to be and where it now is gives rise to an uncertainty in momentum.

     – camel Dec 14 '15 at 11:35
  • @camel the "fabric of the universe" is a general relativity concept. Special relativity has no problems with the commutators and the HUP. The HUP comes out of the commutators for the operators of the quantum mechanical setup. – anna v Dec 14 '15 at 15:56
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No. The Uncertainty Principle has to do with the act of measuring. Basically, you cannot simultaneously measure both position and momentum to an arbitrary degree of accuracy. The more accurately you meausre one, the less accurate your measurement of the other becomes. The uncertainty in momentum , as far as I know, won't result from your not knowing when the particle was at a particular place.

AJK
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  • It does. If you're certain of the momentum of a particle, you'll not be able to know where it is, which somewhat boils down to not knowing when a particle is during a time interval. "the uncertainty principle has to do with the act of measuring" is not enough of an explanation to answer "no" to my question... – camel Dec 14 '15 at 11:31
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The question has not been addressed fully so far. The question is better re-framed as, "Can the Uncertainty Principle be written in co-variant form?" and the answer is yes. For example I can consider the four vectors (x,y,z,ict) and (px,py,pz,iE/c) as conjugate and write the uncertainty relation between them.

Ambar Chatterjee
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