Einstein almost tagged dark energy in the early 1920s
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 …
This topic is closed for new posts.
Huh?
"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!!
Re: Huh?
Programmers know - "Constants aren't, variables don't"
Maybe the universe is expanding at at a constant rate but the time inside is being stretched thinner, so it seems to be accelerating.
We all know that there's only so much time to do anything, usually short by 10%.
Re: Huh?
Hofstadter's law! (as any programming fule kno)
Re: Huh?
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.
Re: Huh?
"that the cosmological constant was a fixed number, or variable."
"A variable constant? That's revolutionary maths right there!!"
or !
Re: Huh?
"...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..."
Re: Huh?
To be fair, some people may also have issue with the grammar, which suggests that the cosmological constant might be a variable, which is a contradiction in terms. Some people use "cosmological term" instead of "cosmological constant" for precisely that reason. (The same occurs with the fine-structure constant, which may in fact vary across space, time, or both, in which case it may be the coupling between electrons and photons but it sure isn't a constant. Fortunately data is still consistent with constancy on this one because the idea of a varying fine structure constant messes with my brain a bit - much more than a varying cosmological constant or a varying gravitational constant.)
Re: Huh?
people just need to engage their brains a bit more! I mean FFS the text was perfectly clear. I am quite angry now.
Re: Huh?
> 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.
Re: Huh?
"i.e. there's an equation, and Einstein integrated both sides of it by some variable (sorry, I don't remember which off hand)"
Space and time coordinates. The equation is actually four equations, one a (covariant) derivative with respect to time and the others (covariant) derivatives with respect to space. Integrate them up and you get a constant multiplied by the metric, since in GR the covariant derivative of the metric is zero.
Re: Huh?
> Hofstadter's law!
The Eighty Per Cent rule.
The last 20% of the project takes 80% of the time allotted. Unfortunately, the first 80% of the project has already taken 80% of the time allotted...
Vic.
Too bad Einstein wasn't around today to use the tools that is available.
A link needs to be spell checked. Erwin SchröDinger
The writer still hasn't öpened the Böx, so anyhting is pössible..
So I wasnt the only one whom noticed mister schraaaaadingers involvement!
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 SchröDinger in my head whenever his name comes up (a bit like I always hear "SkIIIIIIIIIIIIIIIIInEEEEEEEr" because of the Simpsons).
That looks like it has been interpreted and reinterpreted alternatively as ISO Latin 1 and UTF-8 several times...
Was there a cat on the keyboard?
Maybe, and it may be dead. We'll have to have a look...
+1 for the username, good sir!
Are you a Redditor perchance?
Dark matter
Is an embarrassing mystery in Physics. We cannot explain it. We have no clue in how to detect it with experiments in Earthly labs. It's our generation's ether problem, that was solved by relativity. And ditto Dark Energy.
It's a bit embarassing when suddenly we do not know what makes the Universe evolve the way it does in terms of expansion and cosmic dynamics.
Re: Dark matter
How is that "embarrassing"? In front of whom?
The attitude of the Prussian Gymnasium, "know all your answers when the teacher asks you" should be deep-sixed once you leave that lair of scum and villany.
> We cannot explain it.
We cannot "explain" basic QM either.
Re: Dark matter
>> We cannot explain it.
> We cannot "explain" basic QM either.
We can't explain magnets.
Re: Dark matter
...or women...
...And the strange problem of boiling water freezing faster than room temperature water...
Re: Dark matter
The boiling water freezing faster has been explained, or at least explained to the point that there are few arguments about it.
We're still utterly knackered on the first problem though. Tens of thousands of dilligent research and still no closer to understanding.
Re: Dark matter
Magnetic can be reduced to electric fields + relativistic effects though.
Re: Dark matter
Electric fields can be reduced to a Faraday tensor and relativistic projections. In the end it all boils down to a Lagrangian, and everyone can go home happy, or go mad asking why the Lagrangian of the Standard Model is so damned ugly.
Re: Dark matter
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?
Re: Dark matter
> We can explain magnets - you just weren’t paying attention or your teacher was shit.
Wooosh....
http://knowyourmeme.com/memes/fcking-magnets-how-do-they-work
Re: women
He had women figured out, at least well enough to live with his wife and mistress in the same house.
Re: Dark matter
"We can't explain magnets."
I can. But the subject is too repulsive.
, "... a non-observable negative density..."
That's about as comprehensible a description of dark energy as I've heard yet! Sounds like the Hip Einie was there; he just couldn't believe that there was actually any "there" where he was!
Re: , "... a non-observable negative density..."
he just couldn't believe that there was actually any "there" where he was!
That's because it is only true for very large values of wasn't.
But what about the cat?
have either of them bothered to check it?
Re: But what about the cat?
The cat was fine. After Schrödinger put it in the box and closed the lid, Someone in another room saw an empty bag moving, opened it, and let the cat out of the bag.
(Seems Schrödinger forgot to account for quantum tunneling and feline luck.)
Re: But what about the cat?
Ah, but can one cat simultaneously exit two bags in two different rooms?
And does this experiment scale beyond 9?
Re: But what about the cat?
While in principle one cat can exist in two bags in two different rooms - one could set up the experiment by leaving a cat in a room with two bags and not observing into which bag the cat climbed, or by ensuring two bags are in the viciinty of the box in which Schroedinger imprisoned his victim - the breakdown of coherence on large scales leaves this extremely unlikely. Since the probability for a cat to tunnel out of the box into just a single bag is itself extremely small for the same reason, we must conclude that an experiment in which a cat could be let out of one of two bags in different laboratories is extraordinarily unlikely to yield the desired results, even if the physical principles are sound.
Re: But what about the cat?
"and not observing into which bag the cat climbed,"
That's easy, in order
1) the warmest
2) the most comfortable
3) the easiest to get into
4 the hardest to be removed from
Re: But what about the cat?
Even then there is a small probability that the cat would go into the other bag. So basically we've got a stat < cat in bags | = (probability of bag A) * | cat in bag A > + (probability of bag B) * | cat in bag B >. 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. -- but so long as we can quantify the probabilities we can still run the experiment. It would just take an even finer control of the systematics.
Re: But what about the cat?
(ouch. that's | cat in bags >, not < cat in bags |. what i originally wrote makes no sense.)
Re: But what about the cat?
You sir deserve a cookie. Here *passes a cookie*
Re: But what about the cat?
Thank you.
The experiment also works better if we cool the cat down as far as possible. Any small increase in the cat's de Broglie wavelength will be extremely helpful.
Re: But what about the cat?
But cats are pretty cool already, no?
Re: But what about the cat?
As the great philosophical group Squeeze once said “It’s very cool for cats”, though we have not idea with it is that is cool for cats
Re: But what about the cat?
"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.
This topic is closed for new posts.
