Possible Loophole in the Uncertainty Principle?

[Hypercube]

The uncertainty principle states that it is impossible to know both a particle's velocity and location simultaneously. But I discovered a possible loophole in this principle; quantum entanglement. Suppose there were two particles that came from the same point, each going in the polar opposite direction of its partner. Now, according to the quantum entanglement theory, these two particles would both have identicle velocities. Let's say that their velocities are 179 000 miles/sec.

 

Now, since the uncertainty principle forbids us from accurately measuring both the velocity and position of the individual particles, all we could do is accurately measure one or the other. However; since the two particles are entangled, we don't have to measure both particles properties simultaneously. We could have one computer accurately measuring particle A's velocity, while another is measuring particle B's position.

 

Let's say that we draw an invisible line through the point where the two particles came into existence (which we will call 0), all around the sphere so that the two particles are travelling on the line. Now, since particles A and B are travelling in polar opposite directions, if we measured Particle B's position; for clarity sake we will say that particle B's position on the line is

{x,y} = {4000, 0}. Since both particles have the same velocity of

179 000 miles/sec, that would mean that Particle A's position would have to be {x,y} = {-4000, 0}

 

Low and behold, we now know with accuracy both particle's velocity, and position without violating he uncertainty principle.

 

Now I just have to say - since I know that a lot of you are - that I know that this scenario would only be possible in a 100% vacuum environment, otherwise the two particles would be interfered with by other particles. Even so, it still would theoretically work.

[swansont]

The uncertainty principle states that it is impossible to know both a particle's velocity and location simultaneously. But I discovered a possible loophole in this principle; quantum entanglement. Suppose there were two particles that came from the same point, each going in the polar opposite direction of its partner. Now, according to the quantum entanglement theory, these two particles would both have identicle velocities. Let's say that their velocities are 179 000 miles/sec.

 

How do we know this velocity exactly?

 

Now, since the uncertainty principle forbids us from accurately measuring both the velocity and position of the individual particles, all we could do is accurately measure one or the other. However; since the two particles are entangled, we don't have to measure both particles properties simultaneously. We could have one computer accurately measuring particle A's velocity, while another is measuring particle B's position.

 

Let's say that we draw an invisible line through the point where the two particles came into existence (which we will call 0),

 

How do we know this point exactly?

[tomgwyther]

Firstly, I quite like your post, it's worth raising, as Heisenburgs findings always seem to me; a little uncertain.

 

As far as I know, you can messure accurately, one or the other (Velocity-Position)

Thus theorectically you could use two sides of the same particle to messure both?

 

The thing that uneases me about Heisenburg is that, by mesuring useing 'light' he affects the particle. Maybe the device he uses to get a result is at fault?

I've always felt it's like mesuring traffic flow on a highway, by crashing into a few cars.

[Sisyphus]

The thing that uneases me about Heisenburg is that, by mesuring useing 'light' he affects the particle. Maybe the device he uses to get a result is at fault?

I've always felt it's like mesuring traffic flow on a highway, by crashing into a few cars.

 

The uncertainty is the result of both theoretical (the mathematics of the wave function itself) and practical (lack of an adequate "device," like you say) considerations, though either would be sufficient. The practical consideration, of course, is that anything you use to measure is going to have the same uncertainty as the thing you're measuring, as would anything you use to measure that, etc., to an infinite regression.

[Klaynos]

The thing that uneases me about Heisenburg is that, by mesuring useing 'light' he affects the particle. Maybe the device he uses to get a result is at fault?

I've always felt it's like mesuring traffic flow on a highway, by crashing into a few cars.

 

Going at this from a purely mathematical point of view...

 

http://en.wikipedia.org/wiki/Uncertainty_principle#Derivation

 

Which bit of the derivation is not valid?

 

From a physical view, how else can you measure anything? You count cars by firing (or arranging for the sun/street light to fire) photons at the vehicles changing their momentum, and detecting there position using the reflected photons hitting your eye...

[lucaspa]

The uncertainty principle states that it is impossible to know both a particle's velocity and location simultaneously. But I discovered a possible loophole in this principle; quantum entanglement.

 

I think you need to check out whether entanglement involves complementary properties. Heisenberg's Uncertainty Principle involves complementary properties -- position and momentum being one pair.

 

Entanglement that I have seen involves different properties, the ones I have seen most being polarization -- right or left -- and spin -- up or down.

 

These are not complementary but simply 2 states that a quantum particle can be in.

 

You may be trying to use apples to determine oranges.

[someguy]

does anybody know what cause heisenberg to come up with this? How did he arrive at this conclusion?

[Hypercube]

Okay guys, maybe I am wrong about the whole entanglement thing, but I think I am right in saying that if two photons emerged from one point, and travelled away from each other in polar opposite directions; my scenario would work. Since photons always travel at the speed of light, it would mean that both photons' momentum and velocity would be identical, logically this would imply that it would be possible to determine both their positions and momentum simply by analysing one of the two properties on the particle's partner.

[Klaynos]

does anybody know what cause heisenberg to come up with this? How did he arrive at this conclusion?

 

If you search around online you can probably find a copy of his 1920's paper...

 

Okay guys, maybe I am wrong about the whole entanglement thing, but I think I am right in saying that if two photons emerged from one point, and travelled away from each other in polar opposite directions; my scenario would work. Since photons always travel at the speed of light, it would mean that both photons' momentum and velocity would be identical, logically this would imply that it would be possible to determine both their positions and momentum simply by analysing one of the two properties on the particle's partner.

 

The problem is there is uncertainty in their "one point" of origin. Also, above swansont said How do we know this velocity exactly? you've not answered this here. This needs to be addressed, we can't just say "if we can find this" we need a method that this can be found.

[Hypercube]

We are using two photons, we all know that they always travel at the speed of light; 180 000 miles/sec. I should have been more clear which type of particle I meant in my first post.

[insane_alien]

We are using two photons, we all know that they always travel at the speed of light; 180 000 miles/sec. I should have been more clear which type of particle I meant in my first post.

 

then why the hell would you need to measure the velocity?

[Klaynos]

We are using two photons, we all know that they always travel at the speed of light; 180 000 miles/sec. I should have been more clear which type of particle I meant in my first post.

 

How do you measure their position exactly then?

[swansont]

The photon position uncertainty will always be there because you can't localize it any better than the wavelength.

[akashgenius]

im no expert at this but i dont think u can measure the position and velocity of the particle simultaneously as u say it because since the 2 particles are entangled if u try to measure the postion of 1 particle, u disturb it's velocity and at the same time the velocity of the other particle no matter how far apart the particles are. so it comes down to the same reason u cant measure the position and velocity of a singular paticle simultaneously. (plz correct me if im wrong)

[someguy]

as i understand it it is a natural truth that you cannot know the location and momentum of an electron. it is not from difficulty of measurement and it is not because by measuring you will disturb the electron. it is because of what an electron is that you can't do it. personally, so far, i think it may have to do with the speed the electron is traveling at. it is moving so quickly that it pretty much exists in more than one place at once.. like if it was stretched out. if this is the case then you could not know the location of the electron since it is essentially in more than one place at once, but you could know its velocity. or if you take a freeze frame or manage to isolate the actual electron then you have erased information about its speed since it would cease to be in sort of more than one place at once and therefore its speed must have changed. therefore for an electron moving in a straight line you would have a line of improbability where the more you know the speed of the electron the less you know the location and vice versa. I don't know, that's how i see it so far anyways.

[CPL.Luke]

and remember that the standard uncertainty principle that everybody has heard about talks about position and momentum not position and velocity.

[lucaspa]

Okay guys, maybe I am wrong about the whole entanglement thing, but I think I am right in saying that if two photons emerged from one point, and travelled away from each other in polar opposite directions; my scenario would work. Since photons always travel at the speed of light, it would mean that both photons' momentum and velocity would be identical, logically this would imply that it would be possible to determine both their positions and momentum simply by analysing one of the two properties on the particle's partner.

 

Hypercube, there are several problems here:

 

1. Not EVERY pair of properties is complementary. That is your biggest problem. You are assuming that it is impossible to know both of every arbitrary pair of properties. As far as I know, photons don't have "momentum". That is electrons.

2. The most often used complementary properties are POSITION and momentum for electrons in an orbit around a nucleus. It is under those particular conditions that you cannot know both the position and momentum of the electron exactly. http://www.ecse.rpi.edu/~schubert/Course-ECSE-6968%20Quantum%20mechanics/Ch02%20Postulates%20of%20QM.pdf

 

I really suggest you read this article, and other articles on QM on the web, all the way thru.

[bascule]

The uncertainty principle states that it is impossible to know both a particle's velocity and location simultaneously. But I discovered a possible loophole in this principle; quantum entanglement. Suppose there were two particles that came from the same point, each going in the polar opposite direction of its partner. Now, according to the quantum entanglement theory, these two particles would both have identicle velocities. Let's say that their velocities are 179 000 miles/sec.

 

Now, since the uncertainty principle forbids us from accurately measuring both the velocity and position of the individual particles, all we could do is accurately measure one or the other. However; since the two particles are entangled, we don't have to measure both particles properties simultaneously. We could have one computer accurately measuring particle A's velocity, while another is measuring particle B's position.

 

Einstein proposed the same thing. That very idea is the basis of the EPR paradox:

 

http://en.wikipedia.org/wiki/EPR_paradox

 

Measuring any aspect of one particle collapses the waveforms of both. In this sense there is non-local "spooky action" at a distance, instantaneously between the two particles. In observing A, you alter the behavior of B, and vice versa. Thus this apparent loophole doesn't work.

[Cap'n Refsmmat]

1. Not EVERY pair of properties is complementary. That is your biggest problem. You are assuming that it is impossible to know both of every arbitrary pair of properties. As far as I know, photons don't have "momentum". That is electrons.

 

Photons do indeed have momentum.

 

http://en.wikipedia.org/wiki/Photon

[someguy]

and remember that the standard uncertainty principle that everybody has heard about talks about position and momentum not position and velocity.

 

same thing pretty much isn't it? if you can know the velocity you can know the momentum and vice versa.

 

though i don't understand how photons can have momentum without having mass i'm about to read that. oh i see the momentum is given by the wavelength since the wavelength determines capacity to do work, or energy of the photon. i see how this makes sense in relativistic terms but i guess they must have changed the definition of momentum slightly to accommodate for light. the newtonian definition would not allow for a massless object to have momentum. but then again the newtonian way of thinking doesn't think massless things exist either. so i guess position and momentum are substantially different but only when talking about light. so point taken i guess then.

[lucaspa]

Photons do indeed have momentum.

 

http://en.wikipedia.org/wiki/Photon

 

this is why you don't use Wiki as a definitive source. Momentum is mass x velocity. Photons don't have mass, so P = 0 x v = 0

http://en.wikipedia.org/wiki/Momentum (ironic, isn't it?)

 

If you look thru the webpage I cited, they end up doing the same thing for momentum within the QM equations.

 

As far as I can tell, not EVERY possible pair of properties is complementary. Therefore it is possible to know the exact velocity and position of a photon. Only some properties are complementary such that we cannot know the exact value of both properties simultaneously.

[insane_alien]

Momentum of massless objects

 

Massless objects such as photons also carry momentum. The formula is:

 

p = \frac{h}{\lambda} = \frac{E}{c}

 

where

 

h\' date=' is Planck's constant,

\lambda\, is the wavelength of the photon,

E\, is the energy the photon carries and

c\, is the speed of light. [/quote']

 

yes lucaspa, it is ironic.

[swansont]

this is why you don't use Wiki as a definitive source. Momentum is mass x velocity. Photons don't have mass, so P = 0 x v = 0

http://en.wikipedia.org/wiki/Momentum (ironic, isn't it?)

 

What's wrong with the wiki entry? The page you cite gives the photon momentum. "Massless objects such as photons also carry momentum" [math] p = \frac{h}{\lambda} = \frac{E}{c}[/math]

 

That's absolutely correct.

[314159]

Quite right. Of course photons have momentum, which is why ideas such as 'solar sails' were suggested, where the momentum of a photon is harnessed. The equations are exactly as you describe.

hyperphysics page describing momentum of photons

[swansont]

Photons possessing momentum is also the basis of laser cooling & trapping, for which the 1997 Nobel prize was awarded.