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03:25
PSA I fixed LaTeX.
I've set up a build system that enables \ref{namespace.labeled_item}, where namespace is determined by a set of comments at the top of the file declaring which other files to "import" and what namespace to give each one.
 
1 hour later…
04:45
does anybody know why, if q mechanic has so much physics knowledge & is a theoretical physicist, they have such a passion for adding tags ? i know there is debate if they are a bot but I just find this peculiar ....
04:56
So ACuriousMind is an AI and Qmechanic is a bot. Do we have any humans on the site? :-)
@Relativisticcucumber the Planck length is the smallest length that can be measured because to measure a smaller length would require such a high energy density that a black hole with a size of about a Planck length would form.
So one of the suggestions about quantum gravity has been that spacetime is granular at about the Planck length scale because below that it can no longer be described as a smooth manifold.
So the Planck area š“ā‚š² emerges naturally as the discrete unit area of an event horizon, and it isn't surprising to see it appear in the equation for the entropy associated with the horizon.
But bear in mind that to call this sort of thing highly speculative would be an understatement.
i expect (naively) entropy to be related to the system, so it surprised me to see that there is an expression where it is purely related to space? is this because an empty space or a black hole situation would be some kind of limit on entropy so we discuss that case?
also thanks for the response i have been dying to know more about this !
also can you elaborate on what you mean by "spacetime si granular"?
This is one of the weird things bout the black hole entropy. It turns out to be proportional to the area of the horizon i.e. to the radius squared, not to the volume as you'd expect from regular thermodynamics.
This kicked off a speculative area of research generically known as the holographic principle i.e. that the idea that the horizon captures the state of the space inside in the way a 2D hologram can capture a 3D image.
hm well also this seems to make no appeal to what is contained in the space (be it area of volume) - is this not a problem ?
The holographic principle is a tenet of string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the regionā€”such as a light-like boundary like a gravitational horizon. First proposed by Gerard 't Hooft, it was given a precise string-theory interpretation by Leonard Susskind, who combined his ideas with previous ones of 't Hooft and Charles Thorn. Leonard Susskind said, ā€œThe three-dimensional world of ordinary experienceā€“ā€“the universe filled with galaxies, stars, planets, houses...
yeah i came across these questions while watching a lecture on this principle ! it is very interesting
even though i am struggling to wrap my head around it
05:11
You're not the only one :-)
but so i think still the main issue for me is relating entropy to space
because i thought it was about the information or number or states a system can form
but here we dont appeal to the system at all ?
I don't think anyone understands what it means though there are lots of ideas.
Information contributes to the mass of a system, and it's the mass that generates the horizon, so it's not inconceivable that the horizon could somehow capture all the information inside it.
sorry could you elaborate on "information contributes to the mass of a system"
@Relativisticcucumber See:
53
Q: Is a hard drive heavier when it is full?

CasebashBrowsing Quora, I saw the following question with contradicting answers. For the highest voted answer: The bits are represented by certain orientations of magnetic fields which shouldn't have any effect on gravitational mass. But, another answer contradicts that one: Most importantly...

Re your question on the granularity of spacetime, this is known as the spacetime foam idea:
Quantum foam (also known as spacetime foam or spacetime bubble) is a theoretical quantum fluctuation of spacetime on very small scales due to quantum mechanics. Matter and antimatter are constantly created and destroyed. These subatomic objects are called virtual particles. The idea was devised by John Wheeler in 1955. == Background == With an incomplete theory of quantum gravity, it is impossible to be certain what spacetime would look like at small scales. However, there is no definitive reason that spacetime needs to be fundamentally smooth. It is possible that instead, in a quantum theory...
thanks ill read both of these !
05:17
Just ... don't take any of this stuff too seriously :-)
what do you mean by that?
ah sorry im not a bot i can understand things
@Relativisticcucumber This area is based on lots of interesting ideas, but little if anything in the way of hard evidence.
ah okay i see - ill treat lightly haha thanks !
tread *
So anyone can propose a theory and assuming it doesn't contain any glaring mathematical mistakes their ideas cannot be disproved (at the moment).
The result is lots of seriously odd suggestions. e.g. have you heard of the firewall idea?
A black hole firewall is a hypothetical phenomenon where an observer falling into a black hole encounters high-energy quanta at (or near) the event horizon. The "firewall" phenomenon was proposed in 2012 by physicists Ahmed Almheiri, Donald Marolf, Joseph Polchinski, and James Sully as a possible solution to an apparent inconsistency in black hole complementarity. The proposal is sometimes referred to as the AMPS firewall, an acronym for the names of the authors of the 2012 paper. The potential inconsistency pointed out by AMPS had been pointed out earlier by Samir Mathur who used the argument...
or ER = EPR?
ER = EPR is a conjecture in physics stating that two entangled particles (a so-called Einsteinā€“Podolskyā€“Rosen or EPR pair) are connected by a wormhole (or Einsteinā€“Rosen bridge) and may be a basis for unifying general relativity and quantum mechanics into a theory of everything. == Overview == The conjecture was proposed by Leonard Susskind and Juan Maldacena in 2013. They proposed that a wormhole (Einsteinā€“Rosen bridge or ER bridge) is equivalent to a pair of maximally entangled black holes. EPR refers to quantum entanglement (EPR paradox). The symbol is derived from the first letters of...
05:22
oh i think i did hear about this just today actually! and also I heard about an idea that wormholes are quantum entanglement I think
woah hahahah yes
All good fun, but right now just good fun.
i saw these all in Susskind's Oppenheimer lecture
Susskind is really keen on this sort of thing. As physicists reach their greying years they seem to get less concerned about being conventional.
't Hooft has openly said he feels free to consider "speculative" ideas now he's old enough not to be worried about his career.
And quite right too. Good luck to him :-)
ahaha well it is very interesting - I am trying to strike a balance between looking at things that are really interesting and also learning fundamentals and tangible things in order to explore those
there is quite a lot to explore - it's very exciting. i like the summers where I can freely explore so much more than the school year
06:07
Are all wave functions eigenfunctions? In particular, consider the solution to the free particle case.
this form of solution is a linear combination of other solutions, so how does this not contradict the notion that it's an eigenfunction, particularly if it can be expresses as a sum of other functions
shouldnt the eigenfunctions form a basis and, therefore, not be expressable by linear combinations of other functions
> Are all wave functions eigenfunctions?
No, a wave function can be a linear combination of eigenfunctions and this is not an eigenfunction because it is not a solution to the TISE. It is time dependent.
06:35
@SillyGoose we tend to casually say potentials add when what we really mean is potential differences add.
That's because the forces add so the total force is F = Fįµ¢ + Fā±¼ so for some displacement between two points s we get āˆ«ā‚› F = āˆ«ā‚› Fįµ¢ + āˆ«ā‚› Fā±¼ i.e. Ī”V = Ī”Vįµ¢ + Ī”Vā±¼.
Where the Ī”s indicate it's the potential difference we are calculating not the absolute value of the potential.
 
1 hour later…
07:53
@JohnRennie obligatory SMBC
2
 
2 hours later…
09:30
@Relativisticcucumber Serious answer: Tags are essentially the only organizational tool we have to group questions with similar topics together. You can use tags to ignore and highlight questions in the activity feed, and you can restrict searches to specific tags. All this only works if questions are actually tagged with meaningful and appropriate tags, and so Qmechanic's tag edit are a great contribution to searchability of the site.
 
3 hours later…
12:02
All wavefunctions are eigenfunctions
They're eigenfunctions of the identity operator
@JohnRennie We all know you are an android, don't try to hide that :P
 
4 hours later…
16:01
ah thanks i have a larger appreciation for tags now. i will strive to tag better. thanks for explaining. @ACuriousMind
@JohnRennie Thanks for the answer. I am still a little bit confused as to how to apply the superposition principle to electric potential.
16:19
to compute an electric potential, not a potential difference
I have a question about the ether: could not there exist a luminiferous ether which swirls around the sun (in elliptic fashion with the earth) kind of like how Descartes explained it? This way the results of the Michelson-Morley experiment is not evidence against its existence, provided the torque between the closest side of the earth to the sun and the farthest side is a very, very small.
16:41
OKay nevermind I think I understand the electric potential thing.
 
1 hour later…
Jim
Jim
17:49
@Hypernova The widely accepted and thoroughly tested theory of general relativity successfully explains all of the observations of that experiment with no need to involve an ether. Given that it also explains far more than any theory involving an ether, I'm going to go out on a limb and say there isn't one
@Jim I agree with you, and the fact that the assumptions of GR are very elegant, and that thinking of the ether this way is reminiscent of Ptolemy's epicycles situation. But I'll see if I can make a theory of the ether that can explain all measurements. That way, science cannot invalidate it, so it's left to philosophy. lol
Jim
Jim
@Hypernova good luck with that. It's weird to focus on something that didn't work out in the past like that, but if you succeed then I guess everybody wins. If I were you, I'd look for the stuff GR doesn't explain well and see if any other new idea might fill in the gaps, because GR will have to be a special case solution of any more generally applicable theory.
18:04
Are operators represented as matrices in Quantum mechanics generally invertible?
fqq
fqq
18:21
no, any observable for which the result of a measurement can be zero is a not invertible
spin operators for integer spin, annihilation operators are not invertible
 
1 hour later…
19:51
@ACuriousMind obligatory quotation
 
4 hours later…
23:50
What is now often called Lorentz ether theory (LET) has its roots in Hendrik Lorentz's "theory of electrons", which was the final point in the development of the classical aether theories at the end of the 19th and at the beginning of the 20th century. Lorentz's initial theory was created between 1892 and 1895 and was based on a completely motionless aether. It explained the failure of the negative aether drift experiments to first order in v/c by introducing an auxiliary variable called "local time" for connecting systems at rest and in motion in the aether. In addition, the negative result of...
> Because the same mathematical formalism occurs in both, it is not possible to distinguish between LET and SR by experiment. However, in LET the existence of an undetectable aether is assumed and the validity of the relativity principle seems to be only coincidental, which is one reason why SR is commonly preferred over LET.
It's basically Occam's Razor to prefer SR over an ether theory.

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