Question on validity of Heisenberg's Uncertainty principle

[Shan K]

Hi,
I have a question about the validity of Hiesenberg's principle when relativity is in action.
Hiesenberg's principle tells us that simultaneous measurement of position and momentum can not be done accurately . But relativity tells us that simultaneity is relative , so simultaneous measurement in my frame is not remain simultaneous in others' frame . So can they accurately measure the position and momentum?
If they can, then we can transform the data in our frame with the help of lorentz transformation, and we will have the simultaneous position and momentum.
CAN IT BE DONE ?

 

[laudas]

What is position ? If something is moving how can it have a absolute position ?

 

[Shan K]

What is position ? If something is moving how can it have a absolute position ?

I am not talking about absolute position but the position in my reference frame. And in classical physics we can define the position of a particle at each instant of time whether it is moving or not.

 

[atyy]

In non-relativistic quantum mechanics, observables (in the Heisenberg picture) are labelled by time. In relativistic quantum mechanics position is no longer an observable but a label for an observable. So in relativistic quantum mechanics, observables are labelled by position and time. It remains the case that only commuting observables can be measured simultaneously and accurately.

So the short answer is that one has to adjust things a bit to make quantum mechanics work in relativity, but the basic principles restricting simultaneous measurement remain the same.

 

[laudas]

Position is always relative to something, (excuse my use of term absolute position), and how to you get object's position ?
You use a photon ? that photo must have energy which must affect the object your trying to find out about,
As a photon is not of zero size(the one you using to do the measure with), there must be a uncertainty.
So called classical physics dose not take this into account.
The other way of looking at it, all information is energy, the closer the energy of the measurement is to the energy of the particle your trying
to measure, the more affect it will have on that particle.

 

[bhobba]

Hiesenberg's principle tells us that simultaneous measurement of position and momentum can not be done accurately .

That's not what it says. You will find many threads on this forum explaining it.

First there there is no observation that simultaneously measures position and momentum.

Secondly QM is based on the Galilean transformations in which simultaneity is absolute.

Thanks
Bill

 

[atyy]

Position is always relative to something, (excuse my use of term absolute position), and how to you get object's position ?
You use a photon ? that photo must have energy which must affect the object your trying to find out about,
As a photon is not of zero size(the one you using to do the measure with), there must be a uncertainty.
So called classical physics dose not take this into account.
The other way of looking at it, all information is energy, the closer the energy of the measurement is to the energy of the particle your trying
to measure, the more affect it will have on that particle.

In classical special relativity, position and time are only labels - it is the spacetime event that is absolute. In quantum special relativity, position and time are labels for events at which observations occur.

 

[bhobba]

it is the spacetime event that is absolute. In quantum special relativity, position and time are label for events at which observations occur.

Good point. Regardless of relativity the output of an observation is a space-time event. QM says that output can't tell you both position and momentum.

Thanks
Bill

 

[tijana]

Position is always relative to something, (excuse my use of term absolute position), and how to you get object's position ?
You use a photon ? that photo must have energy which must affect the object your trying to find out about,
As a photon is not of zero size(the one you using to do the measure with), there must be a uncertainty.
So called classical physics dose not take this into account.
The other way of looking at it, all information is energy, the closer the energy of the measurement is to the energy of the particle your trying
to measure, the more affect it will have on that particle.

What do you mean by photon is not zero size, that it have mass?
And I was puzzled with the thing that if we say that photons are particles then uncertainty as for other particles are correct. But what does it mean then? Does it mean that E is transporting with some probability?

 

[Nugatory]

Hi,
But relativity tells us that simultaneity is relative , so simultaneous measurement in my frame is not remain simultaneous in others' frame.

Relativity tells us that simultaneity is relative for events happening at different points (to be precise, spacelike-separated events). There is no trouble establishing simultaneity for things happening at the same point and thus no difficulty applying the uncertainty principle here.

 

[Drakkith]

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