# Need Clarification on Uncertainty

• The Rev
In summary, the Uncertainty Principle in quantum mechanics states that we cannot know with certainty both the position and momentum of a subatomic particle. This is a result of von Neumann's 5th postulate and is a fundamental aspect of QM. While we may not be able to know exactly what a particle is doing when not observed, we can calculate the probability of certain outcomes. Heisenberg's uncertainty principle relates the uncertainty in position to the uncertainty in momentum, and states that if one is known with high probability, the other will have a wide range of possible values. This principle has been a fundamental aspect of QM and has proven to be accurate in its predictions.
The Rev
I'm reading "In Search of Shrodingers Cat" by Gribbin, and I've come to the part about the Uncertainty Principle. In describing it, he writes about a subatomic world in which it is impossible to know what particles (such as electrons) are doing when not observed.

My question is, do we have at least some idea of what they are NOT doing? For example, we might not know their momentum, or what their position relative the nucleus might be, but can we at least be sure they aren't having tea parties or smoking dope?

Gribbin makes it sound like they could be spelling out "Humans Suck" when we don't look (or that they might not exist at all), so I need some clarification on what the Principle really means this way.

Thanks.

$$\hbar$$

The Rev

The HUP doesn't have anything to do with "it is impossible to know what particles (such as electrons) are doing when not observed".That is a consequence of von Neumann's 5-th postulate (the state vector collapse).

Daniel.

dextercioby said:
The HUP doesn't have anything to do with "it is impossible to know what particles (such as electrons) are doing when not observed".That is a consequence of von Neumann's 5-th postulate (the state vector collapse).

Daniel.

Just goes to show how little I understand what I'm reading. However, you really didn't answer my question. Do we have some idea what these particles are doing, or could it literally be ANYTHING?

$$\oint$$

The Rev

Literally,according to the 5+1 postulates in the Dirac/traditional/vectors and operators formulation,ANYTHING.

Daniel.

Damn!

Thanks, I think...

*Considering the number of subatomic particles in his body, The Rev fears the worst... (insert picture of 400 quadrillion particles smoking crack and watching Fear Factor here)

$$\infty$$

The Rev

There's no other logical interpretation of that 5-th postulate.It's part of the axiomatical structure.Refute it,and u refute the whole theory...

Daniel.

The uncertainty means that, if we measure a physical quantity, we do not know for certain what the outcome will be. Suppose we setup an experiment to prepare an electron in a certain way and we measure its position (and note the result down). If we do the exact same experiment (under identical conditions) and measure the position the same way as before we might find something different. So we cannot say with certainty what the result of a measurement will be beforehand (there are some exceptions of a technical nature).
But you are right, we have some idea of what they are NOT doing (and thus some idea of what they ARE doing) in the following sense: We cannot know exactly what the result of a measurement will be, but we CAN know what the probability will be of getting a certain outcome (if you throw a die, you know you won't get a 7, but you'll get 1,2,3,4,5 or 6 with some probability. This probability is of a different nature, but it illustrates the idea). So it's not like we cannot calculate anything anymore.

This is uncertainty in QM in general. The uncertainty principle is a little different. Heisenberg's original uncertainty principle gives a relation (we can quantify uncertainty) between the uncertainty of a position of a particle and its momentum. As I said, we CAN calculate the probability we get a specific result. The uncertainty principle says that if we know that the probability of finding a particle in a certain small region of space is very high, almost one (the probability distribution for the particle's position is highly peaked at a certain point), then a measurement on the particle's momentum can give very large varying results (the probability distribution for the particles momentum has a wide spread). The converse is also true ofcourse. This is what Heisenberg's uncertainty principle says.

In 'layman terms': "If we know where the particle is, we don't know it's momentum."
The problem with that sentence is that here you're assuming the particle really HAS a position and a momentum before we measure it, but that's another story. QM makes no hypothesis on this matter, it just tells you how to calculate things and it always works out.

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## 1. What is uncertainty in scientific research?

Uncertainty in scientific research refers to the lack of precise and complete knowledge about a particular phenomenon or process. It is the inherent variability and limitations in data, methods, and understanding that can affect the accuracy and reliability of scientific findings.

## 2. Why is uncertainty important in scientific research?

Uncertainty is important in scientific research because it allows scientists to acknowledge and account for potential errors and limitations in their findings. It also encourages critical thinking and further exploration to improve the understanding and accuracy of scientific knowledge.

## 3. How is uncertainty quantified in scientific research?

Uncertainty can be quantified in scientific research through statistical methods, such as calculating confidence intervals or using error bars on graphs. It can also be expressed qualitatively through discussions of limitations and potential sources of error in research methodologies.

## 4. What are the different types of uncertainty in scientific research?

There are several types of uncertainty in scientific research, including aleatory (inherent randomness or variability), epistemic (due to limited knowledge or understanding), and ontological (due to the nature of the phenomenon being studied). Other types include measurement uncertainty, model uncertainty, and human uncertainty.

## 5. How can scientists manage or reduce uncertainty in their research?

Scientists can manage or reduce uncertainty in their research by using robust and reliable methods, conducting multiple trials or experiments, and incorporating peer review and replication into their studies. They can also improve their understanding and minimize biases through open communication, collaboration, and critical evaluation of their own and others' research.

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