"Where it becomes interesting is how Einstein draws out Schrödinger’s work: it left only the possibilities that the cosmological constant was a fixed number, or variable."
A variable constant? That's revolutionary maths right there!!
It’s of historical interest only, at this point, but an analysis of an exchange between Albert Einstein and Erwin Schrödinger seems to show how close Einstein came to predicting the dark energy problem. In this paper, submitted to Arxiv and described at the Arxiv Blog here, Alex Harvey of City University, New York, examines a …
It's mostly a matter of scale.. The number can change over the whole lifetime of the universe (opening another can of worms, as Einstein noted) , which is a rather vast amount of time. For the here-and-now (or a sufficiently "short" time interval) it can be considered "fixed" and act as a constant. The error you get in your calculation would be insignificant, and be applicable to that specific point in space-time.
It's not unlike the old and tried example where Newtonian mechanics work just fine, as long as you stay well below c. The relativistic portion becomes insignificant, and can be "safely" ignored for practical purposes.
"...it left only the possibilities that the cosmological constant was [either] a fixed number, or variable."
Perhaps that can help the hard-of-parsing understand the wording. I thought it was pretty clear, given the next sentence begins:
"The latter, however, he finds deeply problematic..."
> A variable constant? That's revolutionary maths right there!!
No, it's cromulent.
The cosmological constant arises as a "constant of integration", i.e. there's an equation, and Einstein integrated both sides of it by some variable (sorry, I don't remember which off hand). When you do this, you get a new equation where you introduce a "constant". This means it's a value which doesn't depend on the variable you are integrating by. It may well depend on some other variable, or it could be a fixed number, but in this context you call it a constant of integration. The interesting point is that the process gives you no information at all about the value of that constant.
I thought it was my version of Firefox having another one of its intermittent problems with non-English characters!
The trouble is, I may now always hear SchrÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂ¶Dinger in my head whenever his name comes up (a bit like I always hear "SkIIIIIIIIIIIIIIIIInEEEEEEEr" because of the Simpsons).
We can explain magnets - you just weren’t paying attention or your teacher was shit.
Or are we getting into a new 'creationist' physics era where people pretend something can't be explained by one branch of physics so they can put forward another knowing that 99.999% of the population have trouble working a remote?
"But cats are pretty cool already, no?"
Er, yes and no.
"The experiment will be easiest to run if the probabilities are equal -- so the bags are equally warm, comfortable, easy to get into, hard to be pulled from, inconvenient for whichever human is nearby, on top of something someone is wanting to read, etc."
I also think that it's going to be impossible to get two exact bags and even if there is only an infinitesimal difference between them the cat will choose the best one
"if we cool the cat down as far as possible."
I think you are probably breaking the 5th Law of Thermodynamics
" Any small increase in the cat's de Broglie wavelength will be extremely helpful."
Cats can adjust their de Broglie wavelength, their zero point energy and almost every other parameter. They are also quite capable of emerging from a blackhole ( or any other sort of interesting subterranean space)
All this off-topic for sure but discussing GR at this time of the morning (UK) is a bit heavy.
And seeing as so much of 'stuff' is symmetric in the universe - electrons - protons, upspin - downspin, wave-particle duality all the mesons, baryons, bosons and other stuff that all have counterpart particles...
Then might there not be some form of matter (or unmatter) that emits (for want of a better word) 'ungravity' which is a repulsive force as a counterpart to gravity which is as yet undiscovered but could be pushing stuff apart instead of hauling it together.
"So you get big clumps of something that doesn't interact much except through gravity, and normal matter falls into the potential wells. That way we can actually get the kind of structure we see in the universe (very hard otherwise), get galaxies that spin as fast as we actually observe (they'd fly apart otherwise), and introduce a whole ream of other problems."
sorry but that sounds largely bollocks. noone has ever seen an invisible lump of matter and they just defy common sense. The explanation offered by string theory is much better. we've all see puppet shows where where real thin string can be completely invisible from a distance. So it makes sense that the reason galaxies are held together is because of thin string like structures linking all the stars together. That's also why they are spinning because the strings have all become quantum entangled. I am no steven hawkings but I did do physics at A Level for half a year so this isn't just some uneducated rant.
I didn't mean ACTUAL string obviously so those who downvoted my comments need to get a grip.
If it was actual string all the stars would stay the same distance from each other as they are spinning so no the string must be very stretchy elastic kind. Where does the string come from?? probably it was created in the big bank and subsequently over billions of years has become caught in the stars themselves, much like how a shoelace in a box of earings will over time become snagged.
The string may be black in color which is why we can't see it on the backdrop of space, or possibly transparent.
And the fortuitous typo: "big bank" was icing on the cake. (It was a typo wasn't it?)
Of course you might be a troll, wrapped like a mummy in irony - I mean citing "half a year A level physics" as argumentum ad verecundiam to a professional comologist was worthy of Henry Root - in which case I still thank you, multifold.
Either way you owe me a new kb!
> so much of 'stuff' is symmetric in the universe - electrons - protons, upspin - downspin, wave-particle duality all the mesons, baryons, bosons and other stuff that all have counterpart particles...
You mean like Yin and Yang, good and evil, life and death, Dumb and Dumber...
The need for dark energy is due to a flaw in the thinking of the shape of the universe.
We know mass puts a dint in "space time" but what we ignore is that every action has an equal and opposite reaction.
Between the lumps of mass space time is bulging up, causing the effects we atribute to dark energy.
If you drop a ball in water the amount of water it displaces has to move away.
Same with "space time" except it moves away at the speed of light.
What is at the edge of the universe......I tidal wave of disturbed space time spreading outwards.
oh and the big bang was something 4th dimentional "twanging" space time, and as it jumped back the energy released formed matter etc.. etc.. you can work it out from there.
Granted I dropped out of astro because I couldn't deal with diff eqs and vector calculus, but here's the part I don't get on a conceptual level with regard to the dark matter issue:
Essentially Einstein proposed a multi-dimensional framework inside of which our 4 dimensional exits. Our observations occur within that 4 dimensional framework. So if the missing mass/dark matter is simply another 4 dimensional framework sitting next to us in the multi-dimensional framework, why would we be able to measure something in the 4 dimensional framework? Yes we'd be able to detect affects it is having on our system, but we wouldn't be able to measure it directly. So it really is a sort of new ether in the sense that while we know it's there, we can't really experiment with it, measure it, or understand it. In fact, we're just like the ancient cavemen with one major difference: their block was ignorance that could be corrected, the block we face is an actual physical disconnect. So I see this as a variation on the immovable object vs irresistable force paradox: it's only a paradox because if you assume the one the other doesn't exist.
Thanks for taking the time to write these very substantial and interesting posts. I had to look up a couple of terms (I have a passing familiarity with differential geometry but only a glancing acquaintance with cosmology, so for example the abbreviation FLRW wasn't one I recognized - but Wikipedia took care of that), but on the whole I found it about as easy to follow as one could hope from a few paragraphs in a comments section.
...magnetism is a correction to the electrostatic force, caused by relative motion of the charges. Because charges are moving, there is a Lorentz contraction and the local charge density appears to change, relative to stationary charges. Thus, a force. That explanation always seemed rather neat and final to me, pelase speak up if you have a problem with it.
Also bear in mind some physical "constants" are only such under a set of defined conditions......Change those enough of those conditions.
Its convient to assume the speed of light is a constant (its not) and that its synonymous with "C". However whilst C is a fairly universal constant its only a top bound for the speed of light.
Hubble called for revisiting the entire issue of "universal expansion" in 1948. He didn't like the idea and was dubious about the actual accuracy of the means used to estimate intergalactic distances. If the candles aren't quite as standard as one might wish, error creeps in. That in turn brought the correlation between red shift and any putative cosmic expansion into question. By then Gamow had grabbed to loaf and stuffed it with raisins making a homely metaphor that even English majors could feel they understood.
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