Can someone explain to me, in simple terms...

When you do an experiment in QM you are doing the same experiment multiple times and collecting data. [math]\Delta x[/math] is the standard deviation of these position readings. Similarly [math]\Delta p[/math] is the standard deviation of all the momentum readings. The product of these two standard deviations of measurements is greater than or equal to this number.

Doesn't really mean shit about fuck.

actually it is more than measurements, it is an inherent property of quantum systems.

lol come on please be trolling

>why it means the Universe is indeterministic
it doesn't.

It just means you can't measure things with unlimited resolution if you use photons.

prove me wrong

This can be understood quite easily in microscopes: If you increase the frequency of the light used in the microscope, you can increase its resolution (thus decreasing the uncertainty in position) but by increasing the frequency, the photons impart more momentum to the particle you wish to observe with scope (thus increasing the uncertainty in the momentum).

More generally, the uncertainty principle results because the position and momentum operators do not commute (XP != PX), hence a system cannot be in an eigenstate of both position and momentum simultaneously.

If you've done Fourier Transforms before, you can see that momentum in QM is just the Fourier Transform of position. Thus what you're saying is that a function which is very narrow in position space is quite wide in momentum space.

1/2

2/2

Ot's just a corollary of the Cauchy–Schwarz for quantum observables. It is not about the foundation of the umiverse, but the resolution of simultaneous measurements of the expectation of observables. Spend the 10 minutes deriving it and all ypur questions will be answered.

>German language
rejected

Fucking phone typing. Also do remember that the uncertainty principle can be expanded to any pair of observables, commuting or not. Do it generally - the photon momentum explanations above are intuitive and helpful, but mask the complete implications.

But user, there is no uncertainty in observables which commute. You can see it in the proof the German user posted. The right side is 0 because the commutator is 0.

Back to you retarded neo-nazi.

>theoretical limits of measurement
Uncertainty is a general property, not just a limit to measurement.

Yes, which is an important result. Not least for quantum feedback and control which relies on the simultaneous continuous measurement of commuting observables. Once OP bothers deriving it he may also understand squeezed states.

Just read vol 1 and 2 of this: amazon.co.uk/Quantum-Mechanics-Claude-Cohen-Tannoudji/dp/0471569526

It's comprehensive, and you'll understand your quantum having read it. Asking pointless part questions is a waste of everyone's time.

>and why it means the Universe is indeterministic?
In classical mechanics, you could say that if you know the position and momentum of every particle in existence, then you could theoretically predict the future and that'd obviously mean that the universe is deterministic.

The uncertainty principle shows, however, that you cannot know the absolute position and momentum of a particle. This allows the universe to be indeterministic, but it is no proof.

No, it makes no comment regarding whether the universe may, or may not, be indeterministic. It states that the universe may in indeterminable (under the condition that we have fewer orthogonal observables than degrees of freedom). This does not assert whether or not our train is still on its tracks, but rather whether one can stick one's head out of the window, and stare down to see the rails.

This is the correct post. The uncertainty relations don't tell us anything about causality

Are you merely pretending to be retarded

It's just a result of Fourier Analysis and de Broglie's p=ℏk.

Doesn't delta mean increase?

Here, it means standard deviation

no, i am legit retarded

Back to discriminant UK an US gays

The estimator of the standard deviation is not necessarily equal to the standard deviation
And the uncertainty principle is a much deeper statement than a boundary on measurements

I recommend you read feynman's QED, it's a great little book.

he mentions the uncertainty principle there, and says it was useful for its time. however, we came up with better ways to talk about these strange phenomena, and now you could say it's a bit confusing and not as fundamental.

i agree; i always found it hard to picture , and i could not really explain anything with it. also I always thought it was vaguely related to the observer effect, but again this created more confusion.

>implying you need to read the text to understand the underlying concepts

>we came up with better ways to talk about these strange phenomena
Which are?

im talking about the path integral formulation

How does make the uncertainty principle less usefull

>inherent property of wave-like systems
>wave-like
macroscopic objects don't have wave properties
macroscopic world is at least statistico-deterministic, if not strictly deterministic

in the sense that it is a result, not really a principle.

for example if you want to learn relativity, you will not begin with e = mc^2 , but with einstein's postulates. the equation is just a cool result that follows from them.

Fuck me excuse my English
How does the path integral formulation make the uncertainty principle less useful*

I realise that it emerges from more fundamental properties of the wave function. But the path integral formulation doesn't really give a deeper explanation. If anything it's less fundamental because "the sum of all paths" is only a mathematical tool; particles cannot traverse paths

1) no
2) no

kek

Stop posting and learn some basic mathematics

Finish your degree before posting.

The most simple explanation is that you have to put energy into a system to observe it.

If you could see an electron by looking at it with a single photon, the energy from the photon would cause the electron to behave differently than if you didn't observe it.
Because of this, when you look at something, you can know it's momentum or it's position but not both because after observing it, it no longer has those properties.

so simply put, by observing you're simply stopping it's movement?

No, less drastic. By observing you're changing it's movement

>ITT: we confuse uncertainty principle with observer effect

Yeah bruh electrons are actually orbiting around the nucleus in a clear and defined orbit, it's just that we can't measure it XD

Quantum mechanics is a nondeterministic theory because one of its fundamental principles, the Born rule, instead of telling you what result to expect in a given experiment, only tells you the probability of the possible results. The uncertainly principle is not a fundamental principle; it is derived from the Born rule and other principles of quantum mechanics.

Chaps, stop conflating photonic interaction, or more generally strong measurements, with uncertainty. They're not the same, in terms of source of reasoning they're not even related.

Observation destroying information on a state is not uncertainty, it's destructive measurement - often projective measurement.

Variance is calculated after measuring something you faggot.

>yfw physics and math are the purest forms of philosophy

There's no such thing as an observer effect. I'm sure you're referring to decoherence, which I am not describing.
Your words not mine. In fact, if electrons did orbit, you could know both the position and momentum of an electron for all time, which clearly isn't the case.

>You cannot measure variance though
>Variance is calculated after measuring something you faggot.

ok

you take a long exposure photo of usain bolt
- he is smeared out over 100 pixels, whic corresponds to 10m, from this you can calculate his momentum but not the exact position

you take a very short exposure photo of usain bolt
- the picture is dim, but very sharp, you know exactly where he is, but you cant even say if he is moving or not

You forgot h.

Doesn't this leave room for freedom of the will to still exist?

Do 'you' control the particles? If not then nothing has changed.

>and why it means the Universe is indeterministic

It doesn't mean that, and the universe is deterministic.