Physics Help Forum Calculating Uncertainy

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Nov 15th 2017, 08:10 AM   #11
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 Originally Posted by benit13 I don't think this is a QM question.
Since this is a physics forum and not a math foruma I assumed it was about QM. The term uncertainty does not apply to measurement. You may be thinking about precision and accuracy. Otherwise the terms has no well defined meaning. I.e. see

https://en.wikipedia.org/wiki/Uncertainty
 Uncertainty has been called "an unintelligible expression without a straightforward description". ... Uncertainty of a measurement can be determined by repeating a measurement to arrive at an estimate of the standard deviation of the values. Then, any single value has an uncertainty equal to the standard deviation.

Nov 15th 2017, 08:39 AM   #12
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 Originally Posted by Glavien Thank you that all makes sense, exactly what I was looking for.
If that's the case then I'm confused. Where did this question come from, i.e. from a text?. What precisely do you mean by "uncertainty"? What you appear to have in mind is what is known as an increment, at least that's how its often defined in calculus texts.

Last edited by Pmb; Nov 15th 2017 at 08:58 AM.

Nov 15th 2017, 09:52 AM   #13
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 Originally Posted by Pmb Since this is a physics forum and not a math foruma I assumed it was about QM. The term uncertainty does not apply to measurement. You may be thinking about precision and accuracy. Otherwise the terms has no well defined meaning. I.e. see https://en.wikipedia.org/wiki/Uncertainty
The term uncertainty has a different meaning from precision or accuracy and also words like resolution, that works for both classical and modern Physics (eg QM).

Uncertainty is normally characterised by the statement of a minimum or maximum quantity that must be realised for something to happen or not happen.

If you would like me to expand on that it would be best done in a separate thread.

This thread was about the algebra of uncertainties when you are combining more than one (source) of uncertainty.

Last edited by studiot; Nov 15th 2017 at 09:55 AM.

Nov 15th 2017, 10:50 AM   #14
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 Originally Posted by studiot Uncertainty is normally characterised by the statement of a minimum or maximum quantity that must be realised for something to happen or not happen.
I disagree. Not everyone uses precise definitions for these terms and I think that most people would just associate uncertainty with "something not understood".

This is my opinion in two versions

TL;DR version:

Qualitatively: Does that mug look a bit fuzzy because there's a smudge on your glasses? The mug's colour is uncertain. The mug's shape is uncertain. The mug is "uncertain". Whatever...

Quantitatively:
- you should probably use the term "errors" for measurement uncertainty, calculation errors, systematic errors or anything that uses propagation of errors in quadrature. Basically, use that term for most macroscopic quantities with error bars.
- Use the term "uncertainty" for specifying intrinsic uncertainty terms arising from the system response to the measurements/interactions being made.

Long, boring, wordy version...

Qualitatively...
... uncertainty just means "something we're not sure of". That's pretty vague and open to interpretation when considering something like physics. I've seen it used in many contexts for many things in papers.

When describing a phenomenon or object, it means that the phenomenon or object is not fully understood and something is unknown or imprecise about it. When describing a value, measured or otherwise, it is generally understood by scientists to mean the size of the interval in some relevant parameter space by which that value is considered uncertain, or not known. That is, if the uncertainty on a value is large, then no one can be confident that the value is pinned down to the one specified. However, since "parameter spaces" can be very vague ("big" versus "small"), there's no point worrying about semantics here.

Quantitatively...
... in the case of measurements or calculations, the uncertainty is usually just called the "error". After all, if only we had a perfect measuring or calculation device, we could be more certain that the value we have is the correct one. However, the term "error" implies that the source of uncertainty is some mistake on our part, which, as QM points out, is not always the case. In the case of propagation of errors in quadrature, it is more correct to call them "errors" because it applies to specific kinds of uncertainty associated with measurement errors or systematic errors... You cannot apply propagation of errors to uncertainty terms in quantum mechanics, simply because it is a different beast that requires different mathematics.

In the case of QM, the uncertainty is not associated with "errors" and is instead associated with a fundamental limitation in the ability of measuring devices to find out information independently about a system. That is, there is no perfect "fly on the wall" measuring device for QM systems. The same problem is encountered by macrosopic measurements using very, very poor equipment.

Consider, for example, trying to measure the length of a fragile item by using a hammer. The method is that we move the hammer "a bit" to the right and then swing then hammer down. If the hammer hits something, we repeat, otherwise we stop. The length is then just the number of times the hammer hit the item.

We can all agree that this is an awful way to measure the length of something due to massive inaccuracies and imprecision. However, there is the additional uncertainty caused by the fact that if we hammer the item too hard, we damage it and we might find that the next hammer swing doesn't land because we broke the item being measured.

Therefore, the measurement becomes uncertain by the very nature of our device and the nature of the system being investigated, no matter how accurate or precise the hammer is or its user. The laws of physics respond to measurement attempts and if the perturbation is enough to cause substantial changes to the system, the system has changed and an intrinsic uncertainty arises from that change.

Therefore, since it is impossible to measure something without using something else more fundamental than the fundamental particles, we will always have to deal with cases of intrinsic uncertainty.

Nov 15th 2017, 11:03 AM   #15
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 I disagree.

I said that definition discussions should be in a new thread and you obviously want to discuss this.

So here is a new thread.

What is uncertainty?

(note the above line is the link)

Nov 15th 2017, 01:26 PM   #16
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 Originally Posted by benit13 In the case of QM, the uncertainty is not associated with "errors" and is instead associated with a fundamental limitation in the ability of measuring devices to find out information independently about a system.
That is a common misconception. As I explained in a previous post, in QM the term "uncertainty" is another name for the standard deviation of a set of measured quantities. It has nothing to do with the error associated with an instrument and everything to with the actual quantum state at hand. That means that if you give me a wave function I can tell you the uncertainty associated with an observable (defined through a Hermitian operator) such as position. Even when you can measure an observable with absolute precision the uncertainty may not be zero. The spin of an electron is such an example. So is the number on the face of a die. I explain all of this in a webpage I created for this purpose. See

Probability

Nov 15th 2017, 01:36 PM   #17
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 Originally Posted by Pmb That is a common misconception. As I explained in a previous post, in QM the term "uncertainty" is another name for the standard deviation of a set of measured quantities. It has nothing to do with the error associated with an instrument and everything to with the actual quantum state at hand. That means that if you give me a wave function I can tell you the uncertainty associated with an observable (defined through a Hermitian operator) such as position. Even when you can measure an observable with absolute precision the uncertainty may not be zero. The spin of an electron is such an example. So is the number on the face of a die. I explain all of this in a webpage I created for this purpose. See Probability
Yes, Heisenberg sets a minimum uncertainty for any measurement or knowledge about certain properties.

But as I said this is a minimum. The actual uncertainty may be greater or much greater depending upon circumstance.

But this is not the only use of the term uncertainty.

Another answers the question, what is the minimum accuracy I must know or measure a particular property to conform to a particular circumstance?

Nov 16th 2017, 04:30 AM   #18
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 Originally Posted by Pmb That is a common misconception. As I explained in a previous post, in QM the term "uncertainty" is another name for the standard deviation of a set of measured quantities. It has nothing to do with the error associated with an instrument and everything to with the actual quantum state at hand.
Okay, yes. Thanks for clearing that up. I was trying to explain (rather unsuccessfully) that the uncertainty is a property of the quantum system and you can't get around it by having better measuring equipment. The whole thing about the "fundamental limitation in the ability of measuring devices to find out information independently about a system" was an explanation for something else that I can't remember... It's probably time for me to dig up my old lecture notes and textbooks again to refresh my memory.

 I explain all of this in a webpage I created for this purpose. See Probability
That's a nice description!

 Nov 18th 2017, 03:08 PM #19 Physics Team   Join Date: Apr 2009 Location: Boston's North Shore Posts: 1,195 Glavien - Is there a reason you didn't answer my question about what you precisely meant?
 Nov 20th 2017, 05:58 AM #20 Senior Member     Join Date: Jun 2016 Location: England Posts: 333 I think Glavien got the required answer by post #9 of this thread. It is quite possible he is completely unaware that the discussion rumbled on beyond that point. __________________ ~\o/~

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