Faster than Light?

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Couple of spicy questions:

1. If we new particles position to 99.9999....% or 100%, could the particle move at any speed including speed of light or even faster?

2. If a particle would have probability cloud 1 light year wide and we measured and found a particle at one end and few seconds later on the other end, and again found the particle, does is mean that the particle traveled faster than light or not?

Tachyon.
 

Answers and Replies

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Not even salty.
1) NO; Plus knowledge of the particle momentum would be reasonably uncertain.

2) If you did measure such a particle to know where was within that cloud. And assuming it could re-establish such a wide probability cloud again and be available to be uniquely measured and indentified again as the same particle. It would take about a light year to reestablish such a large probability cloud.

More of a Quantum issue than Relativity.
 
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More of a Quantum issue than Relativity.
Thats funny, because I posted this into QM forum and someone moved it into this forum. :)

Thanks for the answers though!

Tachyon.
 
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1. If we new particles position to 99.9999....% or 100%, could the particle move at any speed including speed of light or even faster?
If I understand your question correctly your are wondering if you knew the position of a particle exactly (a Delta function) then, by Heisenberg's uncertainty principle you would have no knowledge of its momentum (a constant), and therefore you could have any velocity including superluminal velocities. Is that correct?

If so, then you should recall that, while the four-momentum of a particle is unbounded the speed is not. As a massive particle gets asymptotically closer to a speed of c the components of its four-momentum increase without bound.
 
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In other words, the _direction_ of the particle would be totally unknown but the magitude of velocity in any given dimension would never be more than 'c'.

[Edit]
Additionally, knowing the position of a particle with more or less certainty doesn't change the magnitude of its speed at all - only its direction. That's why we can say that a photon is always travelling at 'c' irrespective of what else we know about it. When we talk about uncertainty in momentum of a photon, we're talking about the direction of travel, not uncertainty in the magnitude of velocity.

And yeah, this should be in the Quantum forum.
 
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In other words, the _direction_ of the particle would be totally unknown but the magitude of velocity in any given dimension would never be more than 'c'.

[Edit]
Additionally, knowing the position of a particle with more or less certainty doesn't change the magnitude of its speed at all - only its direction. That's why we can say that a photon is always travelling at 'c' irrespective of what else we know about it. When we talk about uncertainty in momentum of a photon, we're talking about the direction of travel, not uncertainty in the magnitude of velocity.

And yeah, this should be in the Quantum forum.
*uncertainty principle is the statement that locating a particle in a small region of space makes the momentum of the particle uncertain*

I am confused, what does direction have anything to do with its momentum? Isnt momentum the speed at which the particle is going? If the particle goes north or south doesnt change anything or does it?

And again, its not me who moved this thread here :)

Tachyon.
 
TMM
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Momentum has direction.

It's equal to mass (a scalar) times velocity (a vector), so momentum is in the direction of velocity for positive mass.
 
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Right, and the uncertainty relation is talking about position in a certain dimension, and momentum in that _same_ dimension. So if you know a particle's position to within delta_x meters, and you define "x" to be a certain dimension, then the HUP tells you the uncertainty in momentum in that direction. The bottom line is that the more you know where a particle is, the less you know where it's going to be next. But it still has to obey the speed limit and conservation of energy. You can't use the HUP to make particles defy the laws of physics.

You also have to remember that relativistic momentum is governed by gamma*m*v, where gamma is the Lorentz factor used in special relativity. So simply having a very very large momentum does not mean speed is ever faster than light.
 
You can't use the HUP to make particles defy the laws of physics.

But what about the energy time uncertainty relation?Doesn't it violate the conservation of energy principle albeit for infintesimal time intervals?
 
malawi_glenn
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You can't use the HUP to make particles defy the laws of physics.

But what about the energy time uncertainty relation?Doesn't it violate the conservation of energy principle albeit for infintesimal time intervals?
yes, but that is ok, since the energy is given back again.

And QuantumGenie's responce reagarging QM can't defy 'laws' of physics is a tautology I would say :P
 
Couple of spicy questions:

1. If we new particles position to 99.9999....% or 100%, could the particle move at any speed including speed of light or even faster?

2. If a particle would have probability cloud 1 light year wide and we measured and found a particle at one end and few seconds later on the other end, and again found the particle, does is mean that the particle traveled faster than light or not?

Tachyon.

Answ 1: I would not think so, as HUB would prove you wrong.

Answ 2: Quantum teleportation would be the issue here, one particle would have the states of three (as depicted in your points of facts), these particles may pop in and out of existence at random.

Sources: See chaos theory.
 

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