KA's Q&A. This week: What exactly is a "dimension?"

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Re: KA's Q&A. This week: The bottom of reality unseeable?

Postby gorcee » Sat Oct 01, 2011 2:31 pm UTC

PM 2Ring wrote:
I think Xanthir has adequately explained what I was getting at. Of course, 10^34 is much larger than 10^24, but 10^24 is just so large already that it's hard to truly appreciate the effect of another "mere" 10 orders of magnitude.



Here's another way of looking at it. Let's say you're a Strong Safety in an American football team, so you play in the defensive backfield.

Now, your opponent is on offense in the 1st quarter, and they have the ball on their own 10 yard line. Do you re-structure your defense based on the location of your goal line? No. Most passing routes only go out 20 yards max.

They pick up 10 yards. Now they're on their 20. Again, your defensive scheme doesn't change, because your goal line is still really far away.

The strategy for the defensive backfield doesn't really change until the offense is under your 40 or 35 yard line. Why? Because at any point farther than that, the goal line is so far away that your immediate concern is plugging up the receivers some 15-20 yards from the line of scrimmage. Or, in other words, regardless of whether the goal line is 99, 90, or 80 yards away, it doesn't change your strategy in the defensive backfield. At that point, it may as well be infinitely far away.

A more mathematical example is boundary layer flow over a flat plate. Basically, the flow profile looks kind of like the right side of the letter U. At the flat plate, the no-slip condition applies, and the velocity is 0. As you get farther above the plate, the velocity increases, but it only increases as high as the free-stream velocity.

Formally, if you construct this system non-dimensionally (so instead of height in centimeters or whatever, we just normalize it to "units"), then the boundary layer flow only approaches free-stream flow in the limit to infinity.

Practically, however, we know this not to be the case, and we observe a point when the boundary layer flow is equal to the free stream flow within, say, 99.5%. The difference in velocity at that point can be considered to be negligible (we couldn't even measure it if we tried).

As it turns out, you don't need to go out to infinity for this case. All you need to do is go about 5 units above the flat plate to observe a 99.999999% match with free-stream. So, in that case, infinity and 5 are effectively indistinguishable.

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Re: KA's Q&A. This week: What exactly is a "dimension?"

Postby thoughtfully » Sat Oct 01, 2011 3:32 pm UTC

gorcee wrote:Wow I typed up a really big long response and then managed to somehow close the fucking window because touchpads on laptops are the stupidest things ever.

Not as stupid as the touchscreens on "smart"phones!
Anyhow, the dimensions have to be really small for a couple of reasons. If they're big, we'd see violations of conservation of matter/energy. But we don't, at least not to the scales that we can resolve.

For example, say a 2-D being lives in the 2-D universe that is the surface of the water in my drinking glass. Now, I, as a 3-d being, stick a pencil into that glass. What does the 2-D observer see? First a point. Then a small circle, expanding in size, eventually becoming constant.

If the extra dimensions were equivalent to our 3, then we'd see matter popping into and out of existence all the time. But we don't. So they have to be quite very small.

Lisa Randall has been all over lately promoting her new book. Curiously, she's got
a model with large extra dimensions. I kd you not!
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Re: KA's Q&A. This week: The bottom of reality unseeable?

Postby Qaanol » Sat Oct 01, 2011 4:12 pm UTC

gorcee wrote:infinity and 5 are effectively indistinguishable.

/thread
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Re: KA's Q&A. This week: What exactly is a "dimension?"

Postby gmalivuk » Sun Oct 02, 2011 2:11 am UTC

Um, why? In the specific context gorcee was talking about, that is absolutely true.
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Re: KA's Q&A. This week: What exactly is a "dimension?"

Postby Qaanol » Sun Oct 02, 2011 3:20 am UTC

That true statement is the zenith of quality this thread has reached, and I have high confidence that it will not be topped. We may now bask in its glory.
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Re: KA's Q&A. This week: What exactly is a "dimension?"

Postby PM 2Ring » Sun Oct 02, 2011 3:30 am UTC

* high infinities gorcee *

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The physicality of time vis-a-vis "before the big bang."

Postby King Author » Tue Dec 06, 2011 11:59 pm UTC

According to our current understanding of physics, time is physical. It's actually real -- the me of ten seconds ago actually exists, right this instant. It's not merely that time is an illusion caused by the fact that things change, it's a physical (I hesitate to say) "place." Like, if I could travel fourth dimensionally, I could travel to the past or future. Well, at least the past.

So, let's say I've invented a method of travelling along the fourth dimension, and for kicks, let's say this method also allows me to perceive the fourth dimension as plainly as the first three. Out of curiosity, I travel all the way back to the big bang.

What do I see? Some say time itself began with the big bang. If that's true, what would it be like if I were travelling in the fourth dimension? Would it be like running into a wall? What would I see?
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Re: The physicality of time vis-a-vis "before the big bang."

Postby thoughtfully » Wed Dec 07, 2011 2:16 am UTC

You are rendered into your constituent particles by the intense temperatures (or crushed by the pressure) before you get to the point where the Universe is too small for you to fit, which is before you get to the point where Quantum Mechanics screws everything up and leaves us all befuddled and scratching our heads.

There's some speculation that the Universe will "bounce" and time will flow smoothly through to the other side, which would correspond to the contraction phase of an oscillating Universe, or it could continue shrinking down to a scale where space and time cease being meaningful concepts; your "wall".

Or maybe there's a cosmic dragon waiting to eat you!
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Re: The physicality of time vis-a-vis "before the big bang."

Postby Vicious Chicken » Wed Dec 07, 2011 2:21 am UTC

Stephen Hawking has compared the question of what was before the big bang to asking what's north of the north pole; i.e. there's no such place, yet there is no barrier / boundary. So I guess if you took your time machine back to the big bang, you'd find that all "directions" point future-ward? Of course, there are plenty of problems both with time machines and trying to even exist at the precise moment of the big bang.

As you approach the big bang, you'd see space and its contents getting compressed, which would presumably make it harder to travel (or see) farther back. Maybe it'd be like trying to squeeze through a tunnel in the shape of a 1/x function? No specific barrier, but it keeps getting tighter and tighter until at some point you can't go any further.

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Re: KA's Q&A. This week: What exactly is a "dimension?"

Postby doogly » Wed Dec 07, 2011 5:32 am UTC

If you want to use a time machine to ask questions about time, then the time you are talking about is the kind that allows time machines. This is not the kind of time that exists, I would wager.

As for the big bang, we need to know quantum gravity to approach giving answers about what happens there. Not even Hawking can say with certainty that time has a pole rather than a throat or a dissolving into foam or what have you.
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Re: KA's Q&A. This week: What exactly is a "dimension?"

Postby gmalivuk » Wed Dec 07, 2011 6:12 am UTC

To be fair, the "north of the north pole" analogy still does a good job of illustrating why the question might not make sense in the first place, even if that's not actually how time turns out to work.
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Re: KA's Q&A. This week: What exactly is a "dimension?"

Postby doogly » Wed Dec 07, 2011 6:26 am UTC

Right, but there could wind up being a completely different answer. Like, "before the big bang was the big crunch of another universe." Or "before the big bang our universe was sort of like it is now, until a brane slid along another dimension and collided with our brane, the collision sparking big bangs at all points in space." I can't say I find things like these particularly compelling, but they certainly are not options which are unscientific to discuss.
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Re: KA's Q&A. This week: What exactly is a "dimension?"

Postby WarDaft » Wed Dec 07, 2011 10:28 pm UTC

If the universe is infinite, isn't it also possible that there isn't anything close to a beginning at all, and that its just more and more energetic and dense as you go further and further back? As long as its homogeneous or very close it shouldn't cause a black hole, right? Or is there evidence that the entire universe, rather than just the observable universe, was in fact tiny at some point?

It would be absolutely delicious if when people asked what was before the beginning of the universe, the correct answer was "What beginning?"
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Re: KA's Q&A. This week: What exactly is a "dimension?"

Postby doogly » Wed Dec 07, 2011 11:12 pm UTC

People are usually talking about the observable universe. It is absolutely true that that's the only part that big banged. (well that and a little extra that has since left our look-back cone.)
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Re: KA's Q&A. This week: What exactly is a "dimension?"

Postby tooyoo » Thu Dec 08, 2011 10:28 am UTC

So doogly already mentioned this, but maybe it's worth pointing out again:

The "north of the north pole" analogy doesn't quite work. There are quite a few respectable models in (string) cosmology which include the concept of pre-big bang cosmology. If anybody is interested in gory details, you might want to take a look at this review. At least the introduction should be understandable.

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Re: KA's Q&A. This week: What exactly is a "dimension?"

Postby yurell » Thu Dec 08, 2011 10:40 am UTC

tooyoo wrote:So doogly already mentioned this, but maybe it's worth pointing out again:

The "north of the north pole" analogy doesn't quite work. There are quite a few respectable models in (string) cosmology which include the concept of pre-big bang cosmology. If anybody is interested in gory details, you might want to take a look at this review. At least the introduction should be understandable.


I wouldn't say it doesn't quite work, just that it doesn't work for all cosmologies -- for those that do have time starting at the beginning of the Universe, then I think the analogy works quite well. As for pre-Universe cosmology ... testable predictions plz.
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Re: KA's Q&A. This week: What exactly is a "dimension?"

Postby tooyoo » Thu Dec 08, 2011 11:54 am UTC

yurell wrote:As for pre-Universe cosmology ... testable predictions plz.


I'm not a cosmologist, so I'll leave it to the experts. But if you look at page 47 of the review I posted, you'll find:
We have already mentioned that, in standard non-inflationary cosmology, initial conditions have to be fine-tuned to an incredible accuracy in the far past [...], or else it is impossible to explain some of the most striking properties of today’s Universe, such as its homogeneity and flatness.


Moreover on page 3:
The hot big bang model (see for instance [618]), originally thought of as another great success of general relativity, was later discovered to suffer from huge fine-tuning problems. Some of these conceptual problems are solved by the standard inflationary paradigm (see [441, 420] for a review), yet inflation remains a generic idea in search of a theory that will embody it naturally. Furthermore, the classical theory of inflation does not really address the problem of how the initial conditions needed for a successful inflation came about. The answer to this question is certainly related to even more fundamental issues, such as: How did it all start? What caused the big bang? Has there been a singularity at t = 0? Unfortunately, these questions lie deeply inside the short-distance, high-curvature regime of gravity where quantum corrections cannot be neglected. Attempts at answering these questions using quantum cosmology based on Einstein’s theory has resulted in a lot of heated discussions [443, 592], with no firm conclusions.


In other words, the appeal of such models is what is so often appealing in beyond the standard model theoretical physics: You escape fine-tuning of parameters, you obtain mechanisms that explain otherwise seemingly arbitrary theories. And the main reason to use string theory is that the quantum gravity thing is a bit difficult otherwise.

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Re: KA's Q&A. This week: What exactly is a "dimension?"

Postby doogly » Thu Dec 08, 2011 11:59 am UTC

Well, testable predictions for 'north pole' big bangs would also be nice, to be fair.
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Re: KA's Q&A. This week: What exactly is a "dimension?"

Postby yurell » Thu Dec 08, 2011 12:14 pm UTC

Oh indeed ... testable predictions are nice for anything! Or, rather, necessary.
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Re: KA's Q&A. This week: What exactly is a "dimension?"

Postby tooyoo » Thu Dec 08, 2011 12:28 pm UTC

doogly wrote:Well, testable predictions for 'north pole' big bangs would also be nice, to be fair.


True, true. I think we can save ourselves the eternal "string theory & predictions" debate. I merely wanted to point out that this sort of thing can be appealing to those who didn't know.


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