uncertain about uncertainty

[Mitch Bass x]

I've been absorbing a large amount of theories which rely on Heisenberg's uncertainty principle. I thought I understood the uncertainty principle but the theories which rely on the principle seem to be utilizing a part of the principle which I am have a problem accepting AS part of the principle. Simply stated: I understand that the Heisenberg's uncertainty principle is very clear in indicating that there are two properties of quantum particles that are not able to be calculated congruently. Either the velocity or the position but not both. Is this not a result of the human inability to measure both position and velocity simultaneously  due to the effect any measuring device would have on the particle? My ultimate point is that many of the theories that rely on Heisenberg's uncertainty principle are indicative that the Heisenberg's uncertainty principle is "proof" for potential activity to occur, at least on the quantum level, that is totally random, as if, all things the same, there can be multiple outcomes. When I consider what I just wrote I wonder if this is why Einstein wrote "god doesn't play dice" when he expressed his discomfort with the Heisenberg uncertainty concept. If the concept does imply that things can happen randomly, what does this have to do with a particle not being able to have both their velocity and position not both being able to be known at the same time. Is it more than the idea that we have no accurate means to measure OR do particles at the quantum level actually not have both, at the same time, a  definite velocity or position? If I can get a simple yes or no to the following question, I would be most appreciative even if the answer was not followed by an explanation: Does the Heisenberg Uncertainty  principle allow for "random" activity?

[Strange]

38 minutes ago, Mitch Bass x said:

Is this not a result of the human inability to measure both position and velocity simultaneously  due to the effect any measuring device would have on the particle?

No, that would be the observation problem. It is true that Heisenberg himself said this was the reason but quickly realised it was wrong. 

It is not just that we can't measure conjugate pairs (momentum-position, energy-time, etc) accurately, it is more fundamental than that. They don't both exist more accurately.

It is a Fourier transform. So, for example, to have a signal of just one frequency, the signal needs to be of infinite length. If you shorten the signal, the greater the number of different frequencies. So you can either specify an exact frequency or an exact length but not both. 

I'm not sure that the "random" nature of quantum theory is directly related to this. They are both consequences of the theory, not cause and effect. (It is not really random, just that outcomes can only be predicted in terms of probabilities. But it is not like anything can happen.)

[studiot]

1 hour ago, Mitch Bass x said:

Does the Heisenberg Uncertainty  principle allow for "random" activity?

No the uncertainty does not arise for random reasons.

There are two different ways that probability arises in both quantum and classical mechanics (the same in both)

Probability assigned to/ associated with time and position which is the result of a continuous variable

Probability assigned to/ associated with discrete energy states which are the result of a discrete variable.

Which do you want to understand?

The 'uncertainty' of Heisenberg arises for a different reason, do yo uknow what a double integral (area integral) is?

[Mordred]

3 hours ago, studiot said:

No the uncertainty does not arise for random reasons.

There are two different ways that probability arises in both quantum and classical mechanics (the same in both)

Probability assigned to/ associated with time and position which is the result of a continuous variable

Probability assigned to/ associated with discrete energy states which are the result of a discrete variable.

Which do you want to understand?

The 'uncertainty' of Heisenberg arises for a different reason, do yo uknow what a double integral (area integral) is?

excellently appropriate approach. Look forward to this developing on this thread. Also +1 to Strange's  reply

Edited September 12, 2017 by Mordred

[studiot]

Does anyone know what happened to Mitch?

 

Seems strange that he would ask a question and not bother to come back for the answer.

[Vmedvil]

I still say it is a quantum cop out for not having exact answers, measure more certainly damn you, *pulls out a plankscope*

 

Maybe not....... *looks at the structure of quantum foam*

Edited October 17, 2017 by Vmedvil

[swansont]

3 minutes ago, Vmedvil said:

I still say it is a quantum cop out for not having exact answers, measure more certainly damn you, *pulls out a plankscope*

Is that an attempt to be flippant, or do you not understand the physics?

[Vmedvil]

3 minutes ago, swansont said:

Is that an attempt to be flippant, or do you not understand the physics?

Refresh that post, you will get it, on the edit I added a more detailed explanation so that people would know I was joking but do explain the physics if you would like, it is because of virtual particles right?

Edited October 17, 2017 by Vmedvil

[swansont]

3 minutes ago, Vmedvil said:

Refresh that post, you will get it, on the edit I added a more detailed explanation so that people would know I was joking but do explain the physics if you would like, it is because of virtual particles right?

No, not so much. The uncertainties involved are typically well above the Planck scale.

Conjugate variables in physics cannot both have a precise value, because they are Fourier transforms of each other. So the wave function for one variable is tied in with the wave function for the other; as one gets smaller in extent, the other gets bigger. The fact that you have waves tells you that you are going to have uncertainty. If one variable were a delta function, the other would be a constant over all space, i.e. if you know where a particle is, exactly, you have zero information about the momentum. Or vice-versa. It's a feature of wave mechanics, so if that's an appropriate description of nature, then you must have these uncertainties.

[Vmedvil]

1 minute ago, swansont said:

No, not so much. The uncertainties involved are typically well above the Planck scale.

Conjugate variables in physics cannot both have a precise value, because they are Fourier transforms of each other. So the wave function for one variable is tied in with the wave function for the other; as one gets smaller in extent, the other gets bigger. The fact that you have waves tells you that you are going to have uncertainty. If one variable were a delta function, the other would be a constant over all space, i.e. if you know where a particle is, exactly, you have zero information about the momentum. Or vice-versa. It's a feature of wave mechanics, so if that's an appropriate description of nature, then you must have these uncertainties.

So, then it is because of it being a multi-variable calculus equation then?

[swansont]

Just now, Vmedvil said:

So, then it is because of it being a multi-variable calculus equation then?

A specific equation (or class of equations). I can have a multi-variable equations that have no uncertainty relation. The Schrödinger equation is not one of them.

[Vmedvil]

 

39 minutes ago, swansont said:

A specific equation (or class of equations). I can have a multi-variable equations that have no uncertainty relation. The Schrödinger equation is not one of them.

 

So, it is just specific to the fourier summation? My summations never have that problem then again I never apply them to QM directly.

 

I blame that a_k and b_k next to a cosine and sine, that would definitely cause uncertainty, it would cause the most strange looking picture ever and no you would never be able to solve for a_k and b_k without uncertainty in that summation.

Edited October 17, 2017 by Vmedvil

[Strange]

For a waveform to be a single frequency then in the time domain it must be infinite in extent. If you have a shorter pulse, then it will be a mix of frequencies. So the more narrowly specified the width, the less well-defined the frequency, and vice versa. That is the same as conjugate pairs in QM.

[Vmedvil]

28 minutes ago, Strange said:

For a waveform to be a single frequency then in the time domain it must be infinite in extent. If you have a shorter pulse, then it will be a mix of frequencies. So the more narrowly specified the width, the less well-defined the frequency, and vice versa. That is the same as conjugate pairs in QM.

Ya, you would need to know what the Universe uses as its limit would that be C or h otherwise you are making it more accurate than the universe does, lets say that E=hf then h would be the limit right or in the case of Δx = Δt * C then C would does that make any sense, why are we going to infinity on this summation? wait, I am retarded, is that why the uncertainty principal says.

 

Edited October 17, 2017 by Vmedvil

[swansont]

A Fourier transform is used for nonperiodic, continuous functions, so it's more general than the series. But yes, you would typically integrate over all space, because wave functions can extend over all space.

[Dubbelosix]

On 11/09/2017 at 10:18 PM, Mitch Bass x said:

I've been absorbing a large amount of theories which rely on Heisenberg's uncertainty principle. I thought I understood the uncertainty principle but the theories which rely on the principle seem to be utilizing a part of the principle which I am have a problem accepting AS part of the principle. Simply stated: I understand that the Heisenberg's uncertainty principle is very clear in indicating that there are two properties of quantum particles that are not able to be calculated congruently. Either the velocity or the position but not both. Is this not a result of the human inability to measure both position and velocity simultaneously  due to the effect any measuring device would have on the particle? My ultimate point is that many of the theories that rely on Heisenberg's uncertainty principle are indicative that the Heisenberg's uncertainty principle is "proof" for potential activity to occur, at least on the quantum level, that is totally random, as if, all things the same, there can be multiple outcomes. When I consider what I just wrote I wonder if this is why Einstein wrote "god doesn't play dice" when he expressed his discomfort with the Heisenberg uncertainty concept. If the concept does imply that things can happen randomly, what does this have to do with a particle not being able to have both their velocity and position not both being able to be known at the same time. Is it more than the idea that we have no accurate means to measure OR do particles at the quantum level actually not have both, at the same time, a  definite velocity or position? If I can get a simple yes or no to the following question, I would be most appreciative even if the answer was not followed by an explanation: Does the Heisenberg Uncertainty  principle allow for "random" activity?

 Ah, a thread, maybe on the same chapter but certainly, not on the same page as my other thread, that is, are things actually random in nature?

 

The uncertainty principle was not really a theory of randomness, it was about the information we can gain at the expense  of a complimentary observable. This view is quite different to the idea that things have to be inherently random. Even a decay process does not need to be random, we can make it entirely deterministic by rearranging the energy levels of an atom, a process known as the quantum zeno effect, which is actually a special case of decoherence which also involves a concept of entanglement. 

On 17/10/2017 at 8:38 PM, swansont said:

A Fourier transform is used for nonperiodic, continuous functions, so it's more general than the series. But yes, you would typically integrate over all space, because wave functions can extend over all space.

 

Though, technically speaking, a lot of physics may not even pertain to this ''infinite phase space.'' Certainly, the finite Hilbert space is attractive for physical reasons. 

On 17/10/2017 at 7:12 PM, Strange said:

For a waveform to be a single frequency then in the time domain it must be infinite in extent. If you have a shorter pulse, then it will be a mix of frequencies. So the more narrowly specified the width, the less well-defined the frequency, and vice versa. That is the same as conjugate pairs in QM.

Can you continue a bit on the bit I highlighted, I would like to know why you said this? There are actual physical reasons in physics, situations in which you can make the radius of a particle go to zero, it will experience infinite self energies. I would like to know in what situation does a frequency become infinite in extent? Is it some classification of an infinite dimensional space, like you might encounter in some exotic idea's about Hilbert space?

Edited October 26, 2017 by Dubbelosix