# The Lego Theory

Discussion in 'Physics & Math' started by Prosoothus, Nov 13, 2002.

1. ### CrispGone 4everRegistered Senior Member

Messages:
1,339
Hi Frencheneesz,

"Well, sort of. Probability is only perfectly precise after an infinite amount of time (in theory). The closer to infinity the amount of data is, the more precise it is. If you take only 3 samples, most likely they will not be quite as precise as maybe 3 million samples."

Ok, what you are referring to here is the Law of Large Numbers, which (in its weak form) states that an average over an infinite number of samples is equal to the expectation value of the underlying probability distribution.

Note the subtle difference with your statement: if you repeat the same experiment over and over, and see the probability for an event as the frequency that that event occurs, then this probability will indeed be dependent on the number of experiments performed, hence the probability is "not exact" (in the sense that in the end it will converge to the underlying probability distribution). What quantum physics tells you is exactly that underlying probability distribution, and that is the "exact" probability distribution (i.e. the one that gives rise to the values of the measurements). The stochasticity

Bye!

Crisp

3. ### chrootCrackpot killerRegistered Senior Member

Messages:
2,350
The most recent verification that we live in a flat space is that galaxy counts follow a 1/r^2 law with increasing distance. If space were curved differently, we'd detect more far galaxies (positive curvature) or fewer far galaxies (negative curvature).
Cosmology, and our predictions of the future of our universe.
No. Not "sort of." The probability of heads vs. tails is, in fact, precisely 50%. You can't precisely measure this probability without taking an infinite sample. That doesn't mean the probability isn't precisely 50% -- it still is.
I have serious doubts about the validity of string theory as well.
We certainly don't know all there is to know about physics, but we do have reason to believe we've found the most fundamental layer -- that of the leptons and quarks. There is mathematical and experimental evidence that these particles are indivisible (and probabilistic).
Perhaps. The difference rapidly becomes semantic for the coin.
String theory refers to dimensions whose components can take on only very small values. In other words, dimensions that don't appear to us macroscopically, because their values are always very tiny. I suppose you could call the observed variance a "width," but it's not really the idea Prosoothus was pushing.

- Warren

5. ### overdozehumanRegistered Senior Member

Messages:
310
But even if you reject local hidden variables, and furthermore dismiss nonlocal hidden variables, you must still then accept the nonlocality of wavefunctions. IOW, once the wavefunction of one of the entangled particles collapses, the wavefunction of the particle on the other side of the universe collapses simultaneously. This is nonlocal interaction, and I don't see how it helps avoid nonlocality in the theory.

7. ### James RJust this guy, you know?Staff Member

Messages:
34,678
overdoze,

You're right. It doesn't eliminate non-locality in the wavefunction. However, it is important to remember that quantum entanglement cannot be used to transmit information faster than light.

8. ### ProsoothusRegistered Senior Member

Messages:
1,973
chroot,

Gee, chroot, that's some proof you got there. Does that mean that the electromagnetic interaction is the result of curved space since it follows the 1/r^2 law, as well????

Tom

9. ### chrootCrackpot killerRegistered Senior Member

Messages:
2,350
Gee, Prosoothus, it sure is unusual for you to misunderstand and fail to recognize the implications of experiments.

If I were to tell you that the products of weak decay most frequently move away from south magnetic poles, would you understand the deeply profound implications? I doubt you would.

- Warren

10. ### FrencheneeszAmazing MemberRegistered Senior Member

Messages:
739
----------As a side question: What does curvature of space effect besides gravity?
--------------------------------------------------------------------------------

"Cosmology, and our predictions of the future of our universe. "

I don't see what your getting at with this, but I did realize one answer to my question: If space is curved, the distance between two points is elongated.

"The probability of heads vs. tails is, in fact, precisely 50%."

Ya, your right. However, I remember at one time the argument of the idea that what can't be measured does not exist was used against me. I disagreed.

"I have serious doubts about the validity of string theory as well."

Granted, but why?

"There is mathematical and experimental evidence that these particles are indivisible (and probabilistic)."

There are things that are probabalistic and not fundemental thus invalidating that arguement (you have mentioned alpha decay in a nucleus which is certainly not fundemental). At one time, we thought atoms were indevisible, why should we say leptons are fundemental just because we lack the power to break them apart and detect whats inside?

11. ### FrencheneeszAmazing MemberRegistered Senior Member

Messages:
739
Prosoothus:

"Does that mean that the electromagnetic interaction is the result of curved space since it follows the 1/r^2 law"

Since chroot would rather insult you than explain why YOUR insult was rather stupid, I will go ahead. The inverse sqare law argument needs not have anything to do with gravity or a force. Curved space would be "longer" than flat space. This means that if we can somehow detect a change in distance in a strong gravitic field, then we can prove that gravity is caused by a curvature in space.

Chroot:

"If space were curved differently, we'd detect more far galaxies (positive curvature) or fewer far galaxies (negative curvature)."

What exactly do you mean by "more far galaxies"? What exactly are you implying?

"If I were to tell you that the products of weak decay most frequently move away from south magnetic poles, would you understand the deeply profound implications?"

What are they?...

12. ### chrootCrackpot killerRegistered Senior Member

Messages:
2,350
It is assumed (based on strong evidence) that the universe is homogenous at large scales, and as such there should be a roughly equal number of galaxies in any large volume of space you investigate.

Count galaxies as a function of distance. A larger radius sphere should include more galaxies. The number of galaxies in a sphere of radius r will be proportional to r^3 in a flat (uncurved) space. (I apologize, I made a typo, r^2, in my last post).

If your count increases faster than r^3, the universe is negatively curved. If your count increases slower than r^3, the universe is positively curved.
Parity is not conserved.

- Warren

13. ### WhiteKnightRegistered Member

Messages:
23
You forgot the .000001% of 'edge', silly!

Good job with everything else, though. Crackpot 'physicists' are so much fun...

14. ### thedIT GopherRegistered Senior Member

Messages:
1,105
One of the results of General Relativity is a set of equations relating several observables in the Universe. Things like mass, age, density. These are the Einstein Field Equations.

They where first solved by Friedman, Robertson and Walker so are called the FRW solutions. They found that the Universe can have 3 possible geometries based on how much mass their is in it. Remembering that mass curves spacetime.

Either,

<ul>
<li>There is not enough mass to halt expansion, space has a positive curvature and is non-euclidean. This is the 'open' solution.
<li>There is enough mass to halt expansion and cause contraction. In this space as negative curvature and is also non-euclidean. This is the closed solution.
<li>The self gravity of the mass exactly counteracts expansion to that it expands asymptoticaly. In this case space is euclidean and is the 'flat' solution. It is also referred to as the critical density case.
</ul>

By Euclidean I mean obeying euclids geometry. Any sufficiently large triangle, say, would obey Pythagoras' theorem. If space is non-euclidean, or Reimannian, this would not happen. It also means the distribution of Galaxies would be noticeably skewed.

All the evidence, there is some that contradicts this though, so far points to space being flat and we live in a Universe that will expand asymptotically.

So the simple is, the curvature of space directly affects the Universe we live in.

15. ### ProsoothusRegistered Senior Member

Messages:
1,973
Frencheneesz,

Chroot used the inverse square law of gravity as proof that gravity is the result of curved space. I then pointed out (through my question) that the electromagnetic interaction follows the inverse square law as well, which would contradict his arguement since most physicists would agree that the electromagnetic interaction is NOT the result of curved space. Why exactly was my question "stupid"???

Also, how would you measure a "change in distance" in a strong gravitational field??

Tom

16. ### chrootCrackpot killerRegistered Senior Member

Messages:
2,350
Uhhh... no, I didn't.
Your response had basically nothing to do with my statement -- because you failed to understand my statement. That's why your question was stupid.

All I said was the following: "Count galaxies as a function of distance. If the number grows slower than r^3, space is positively curved. If the number grows faster than r^3, space is negatively curved."

- Warren

17. ### FrencheneeszAmazing MemberRegistered Senior Member

Messages:
739
"Chroot used the inverse square law of gravity as proof that gravity is the result of curved space. "

He was proving that we living in "flat" space. He did not try to prove anything about gravty. Although I don't see the relevance of flat space chroot....

"Why exactly was my question "stupid"???"

Because it was sarcastic and showed you did not understand chroots statement.

I won't put words in chroot's mouth, but what I was talking about was how you COULD prove that gravity is RELATED to change in geometry. How would you measure change in distance you say? Well lets say you had two FIXED points that you knew the distance between and you introduced gravity into the system, you could then simply measure the distance between those two points and see if they are farther apart, say, with a ruler.

18. ### ProsoothusRegistered Senior Member

Messages:
1,973
Frencheneesz,

If space really does curve, wouldn't the ruler curve with it???

Tom

19. ### FrencheneeszAmazing MemberRegistered Senior Member

Messages:
739

Ya, his answer kinda sucked. It had SOMETHING to do with curviture of space, yet did more to give evidence that it doesn't curve. Of course my question was a bit vauge, although I think I did provide the context of his quote above it...

"If space really does curve, wouldn't the ruler curve with it??? "

Sure itll curve. The point is not that space curves, but that it gets longer. A curved line is LONGER than a straight line between the same two points. The ruler can't just get longer (well... don't make me think about that), so the ruler will measure a longer distance, a curved distance no doubt, but thats how we could prove it. Of course there is always the possibility that space does more weird stuff that makes the ruler longer with the space, or blah blah blah. Do you get it now?

20. ### chrootCrackpot killerRegistered Senior Member

Messages:
2,350
You said you weren't aware of any experiments that can detect the curvature of space. I provided an example of one. How did my answer suck?

- Warren

21. ### FrencheneeszAmazing MemberRegistered Senior Member

Messages:
739
Chroot,

well, I guess your right. But, like I said, my question was kinda vauge and I might not have fully understood the quote I picked out. I was going for evidence that space DOES curve, as under a field of gravity. I think thats what prosoothus thought too.