Brian, I fear this is a "smoke and mirrors" answer that is in fact a non-answer. If you think I'm wrong about that, please could you restate it in simple English. — John Duffield6 hours ago
@JohnDuffield You want me to restate it in terms that you understand?
So you're admitting to not understanding the basic mathematics of spacetime?
From 't Hooft's String Theory lecture notes on page 8 (paraphrased):
To understand hadronic particles as excited states of strings, we have to study the dynamical properties of these strings, and then quantize the theory. At first sight, this seems to be straightforward. We have a string with...
@ACuriousMind : not when the "proof" relies upon a definition. See this: Definition 2. A spacetime is said to be isotropic if at each point there is a congruence of timelike curves. It's curved because... it's curved!
@0celo7: note your confusion between space and spacetime. Pay careful attention now: "The FLRW metric starts with the assumption of homogeneity and isotropy of space". This confusion is endemic, and fatal.
I will leave the original post for historical reference, but as mentioned in the Update below, all four bookmarks are located on this installation page. There are four bookmarks:
start ChatJax installs MathJax and starts a loop that renders $\LaTeX$ as needed.
This is intended for use in chat, ...
@0celo7: now repeat after me: spacetime is not space. Curved spacetime = inhomogeneous space. The space in the room you're in is inhomogeneous, not curved. When you plot this inhomogeneity, it's curved. And your pencil falls down. That space is not isotropic!
When space is neither homogeneous nor isotropic, what you've got is a gravitational field. Curved spacetime. When space is homogeneous and isotropic, what you've got is no gravitational field. Flat spacetime.
@0celo7 : you can't explain it in plain English, and you don't even understand the difference between space and spacetime. The FLRW metric starts with the assumption of homogeneity and isotropy of space. And your definitions were a spacetime is said to be spatially homogeneous if and a spacetime is said to be isotropic if...
@0celo7 : I'm not confused, you are. Now go and read what Einstein said. When space is homogeneous, there is no gravitational field. So spacetime is flat. As in not curved. Your definition says spacetime is flat and yet... it's curved!
@0celo7 : you confused spacetime with space, like Sleareah does, and others, including Wheeler. Einstein never did. The FLRW metric talks about space, not spacetime. Einstein said a gravitational field was a place where space was neither homogeneous nor isotropic. This is modelled as curved spacetime. So when space is homogeneous and isotopic, there is no spacetime curvature.
Why do you think WMAP evidence indicates the universe is flat? Why do you think the universe did not collapse due to gravity when it was small and dense?
@0celo7 No. You worry too much. He's hung up on the fact that you are talking about homogeneous and isotropic spacetimes in your definitions when honogeneity and isotropy are merely properties of the spatial part, but since your definitions reflect that, it's just a matter of taste if you call the spatial part or the spacetime homogeneous/isotropic.
In any case the application of up or down votes is more or less plenary. If Joe Q. Normal wants to downvote that post and has the downvote privilege then they get to.
@0celo7 Voting is anonymous by design, you don't get around that.
user41796
@dmckee And even if a comment was left to the effect of "-1 simply because", you still don't know that it was that user that clicked the down arrow. I've seen many cases of a "-1" comment without any accompanying vote.
@0celo7 We try to discourage people from thinking that thye "know" who voted one way or another because it leans to unnecessary conflict. In any case, you won't be able to penetrate the anonymity unless the culp^H^H^H^Hvoter fesses up.
I think dmckee's main point is to not make assumptions short of ironclad proof. Especially when there's already a measure of tension between two people. Those assumptions don't help resolve matters.
"If you are a good economist, a virtuous economist, you are reborn as a physicist. But if you are an evil, wicked economist, you are reborn as a sociologist."
Update: According to this wikipedia article, blackbody radiation is just thermal noise (Johnson–Nyquist noise); if that's what I'm looking for, what does it sound like?
If a blackbody has a temperature such that its peak frequency was well within our audible range, for example 1 KHz, what would ...
@DanielSank nothing much.. I have paused my exciting transfer project and now coming back to it... I am also trying to learn FRET.. Do you know anything about it?
From 't Hooft's String Theory lecture notes on page 8 (paraphrased):
To understand hadronic particles as excited states of strings, we have to study the dynamical properties of these strings, and then quantize the theory. At first sight, this seems to be straightforward. We have a string with...
