23
votes
When an electron hits a fluorescent screen mounted on a spring, why can't we get both position and momentum?
If I understand you correctly you have an experimental
setup like this.
(image partially taken from The Physics of Springs)
You measure two things:
the $x$ position
given by the position where the ...
- 27.6k
23
votes
Accepted
What relationship, if any, exists between Heisenberg's uncertainty principle and this general principle of uncertainty?
3B1B's Youtube video mainly talks about the
Fourier uncertainty principle
between a function $\psi(x)$ in position space
and its Fourier transform $\hat\psi(\xi)$ where $\xi$
is the spatial frequency ...
- 27.6k
22
votes
What happens when a laser beam is stuck between two mirrors and the distance in-between is decreased gradually? Heisenberg Uncertainty Principle
I will add yet another answer, which would be the most accurate to your description of a laser beam bouncing between 2 mirrors (if starting from "macro" distances), albeit my lack of time ...
- 1,018
20
votes
Accepted
Can Heisenberg's uncertainty principle be used to prove the electron can't exist in the nucleus in this way?
It’s a mistake to invoke relativity on the speed $v$ without also using the relativistic momentum $p$. But if this is a text for students who may be a little weak on relativity, it’s perhaps a ...
rob♦
- 74.3k
15
votes
Does this video from Veritasium imply that the uncertainty principle is false?
No, the video does not imply that the uncertainty principle is false.
But it does imply that you have to be careful/precise to claim what the uncertainty principle is about. It is actually a claim ...
- 7,781
14
votes
What relationship, if any, exists between Heisenberg's uncertainty principle and this general principle of uncertainty?
It is very easy to be seduced by the analogy between Fourier pairs like $x$ and $p$ and the HUR but the relation is basically coincidental.
It is true that $x$ and $p$ satisfy Fourier-type relations ...
- 39.5k
13
votes
Does uncertainty principle apply to holes/gaps in matter?
Holes in semiconductors move as electrons do, but act as if they were positively charged particles. The question really is, are quasiparticles, with an electron "hole" being one type, ...
- 25.6k
12
votes
Accepted
Why Heisenberg's Uncertainty Principle?
There are laws that allow the energy transfer between EM radiation and charged particles to be predicted when they collide; but it yields probabilities applicable to large numbers of interactions ...
- 75.1k
11
votes
Does uncertainty principle apply to holes/gaps in matter?
Yes, the uncertainty principle does apply to holes/gaps in matter.
The uncertainty principle between position and momentum is very general. It follows from the fact that the observable we call ...
- 51.4k
11
votes
Accepted
Do the mean lifetimes of short-lived particles follow a Gaussian (or 'normal', or 'standard') distribution? When plotted?
Yes, indeed, the average lifetime will tend to the normal distribution, as required by the Central limit theorem. A caveat: one has to distinguish between the distribution of lifetime and the ...
- 40.8k
10
votes
What happens when a laser beam is stuck between two mirrors and the distance in-between is decreased gradually? Heisenberg Uncertainty Principle
A similar experiment is what I call quantum fly. The classical fly problem is well known:
From point A and point B two trains depart simultaneously towards each other along the same track with speeds ...
- 40.8k
9
votes
Can Heisenberg's uncertainty principle be used to prove the electron can't exist in the nucleus in this way?
The solution given here is wrong. It uses the non-relativistic expression for momentum, and then compares the velocity with the speed of light, which is the velocity limit of relativistic mechanics. ...
- 26.7k
8
votes
What happens when a laser beam is stuck between two mirrors and the distance in-between is decreased gradually? Heisenberg Uncertainty Principle
Note: the following was intended as a response to a question posed in the comments of a previous answer ("why does the force increase as we move the mirrors together?"), not as a complete ...
- 9,164
8
votes
A question regarding commutators in quantum mechanics
It would be far simpler to just directly measure $x$ of your first beam and $p_x$ of the second beam.
Both of which, $x$ and $p_x$ can be measured to arbitrary precision thus violating the ...
- 14.6k
8
votes
Do the mean lifetimes of short-lived particles follow a Gaussian (or 'normal', or 'standard') distribution? When plotted?
A particle's lifespan is has a memoryless and hence exponential distribution. If $\tau$ is the mean lifetime, the lifetime has CDF $1-e^{-t/\tau}$ (so the half-life is $\tau\ln2$) and PDF $\frac{1}{\...
- 22.4k
8
votes
Accepted
Wrong formulation of Heisenberg's uncertainty principle
Don't be confused. It is definitely $$\Delta E \Delta t \geq \frac{\hbar}{2}$$.
Your professor typo'd here, as if what he wrote: Then we could measure energy with any arbitrarily small error. We want ...
8
votes
Confusion regarding Heisenberg Uncertainty Principle
The operators X and P in quantum mechanics are postulated to lead to probabilities for real-life measurements of position and momentum. In real experiments, those quantities are measured in a pretty ...
- 4,281
7
votes
Accepted
Physical interpretation of Uncertainty
when I operate it on a state $|ψ⟩$ there will be some error every time I measure it
This is a common misconception. Performing a measurement on a system is not mathematically represented by applying ...
- 53.8k
7
votes
Does uncertainty principle apply to holes/gaps in matter?
Holes are not empty space
"Free electrons" and holes in a semiconductor are quasiparticles, that is excitations of a multi-electron system (which are mathematically identified as poles in ...
- 40.8k
7
votes
A question regarding commutators in quantum mechanics
You are assuming that the two beams of electrons are two different systems in identical quantum states. The uncertainty principle limits measurement of two non-commuting observables on one system, but ...
- 21.4k
7
votes
Accepted
How is spooky action at a distance measured?
In general, for entangled spin pairs magnetic fields are used.
But it's important to note that the states are not the same, as you have stated, but are actually anticorrelated.
So for two entangled ...
- 25.6k
6
votes
Accepted
How much is the inherent quantum-mechanical uncertainty in the definition of the second?
tl;dr: It is not currently a factor limiting the ultimate precision of how closely you can make a system oscillate to that defined frequency. To address your question specifically: each atom will ...
- 789
6
votes
A problem with the uncertainty principle
There are two issues with your question.
First the uncertainty principle does NOT state that there is no state where $A$ has a definite value. It states (somewhat loosely) there is no state for ...
- 39.5k
6
votes
When an electron hits a fluorescent screen mounted on a spring, why can't we get both position and momentum?
Thomas Fritsch's answer covers the fact that your experiment doesn't probe the essential problem. So what is the essential problem?
Your measurement system can record whatever it records to whatever ...
- 5,506
6
votes
Accepted
Uncertainty principle manifesting in $j(j+1)$ vs $j^2$
The following two operators $A$ and $B$ have the properties that:
$A$ and $B$ do not commute;
$A^2 + B^2$ commutes with both $A$ and $B$; and
the largest eigenvalue of $A^2$ equals the largest ...
- 38.8k
6
votes
Accepted
Uncertainty Principle in 3 dimensions
If you choose any direction in space, the 1D uncertainty principle applies in that direction. So, if you know the component of a particle's momentum in that direction well, you cannot know its ...
- 5,506
5
votes
What happens when a laser beam is stuck between two mirrors and the distance in-between is decreased gradually? Heisenberg Uncertainty Principle
Let me propose that from a mathematical point of view this question has nothing to do with quantum mechanics. You have got a standing wave between two fixed boundaries (a vibrating string is a ...
- 443
5
votes
Can Heisenberg's uncertainty principle be used to prove the electron can't exist in the nucleus in this way?
The uncertainty principle is about x and p being Fourier pairs. That is, the standard deviation (loosely called the uncertainty) of the position of the wavefunction times the standard deviation of the ...
- 187
5
votes
When an electron hits a fluorescent screen mounted on a spring, why can't we get both position and momentum?
When an electron hits the screen, it will give us a spot of diameter $\Delta x$, whereas the compression of the spring is also measured with a certain precision, which will limit the precision of ...
- 40.8k
5
votes
I want to know something about Heisenberg uncertainty principle
The problem is: if you repeat the exact same experiment with the exact same initial conditions, you will (in all probabilities) get a different value of $x$ and a different value of $p$. Thus, after ...
- 39.5k
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