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Why Understanding Space Is So Hard

nautil.us

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Re: Why Understanding Space Is So Hard

#71

Post by danbruc »

CPLX wrote: post #43

Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space.

52! is the number of different ways you can arrange a single deck of cards. Let's try to wrap our puny human brains around the magnitude of this number with a fun little theoretical exercise. Start a timer that will count down the number of seconds from 52! to 0. We're going to see how much fun we can have before the timer counts down all the way.

Start by picking your favorite spot on the equator. You're going to walk around the world along the equator, but take a very leisurely pace of one step every billion years. Make sure to pack a deck of playing cards, so you can get in a few trillion hands of solitaire between steps.

After you complete your round the world trip, remove one drop of water from the Pacific Ocean. Now do the same thing again: walk around the world at one billion years per step, removing one drop of water from the Pacific Ocean each time you circle the globe. Continue until the ocean is empty.

When it is, take one sheet of paper and place it flat on the ground. Now, fill the ocean back up and start the entire process all over again, adding a sheet of paper to the stack each time you’ve emptied the ocean. Do this until the stack of paper reaches from the Earth to the Sun.

Take a glance at the timer, you will see that the three left-most digits haven’t even changed. You still have 8.063 × 10⁶⁷ more seconds to go. So, take the stack of papers down and do it all over again. One thousand times more. Unfortunately, that still won’t do it. There are still more than 5.385 × 10⁶⁷ seconds remaining. You’re just about a third of the way done. [1]

Well, the volume of the visible universe is 3.4 × 10⁸⁰ m³ and therefore another factor of 4.2 trillion larger than 52!. And then the entire universe is estimated to be at least another 150 or 250 times larger than the visible universe. In diameter, not volume.

[1] http://czep.net/weblog/52cards.html

Re: Why Understanding Space Is So Hard

#72

Post by contravariant »

vectorjohn wrote: post #28
gizmo686 wrote: post #22

Earlier quoted context omitted.

My understanding is that we have conducted experiments to measure the curvature of the universe, and come up with answers that are withing the experimental error of being flat. Without any theoretical reason why the universe should be flat, it is still possible that the universe is curved, but to slightly for us to detect, however, but the simplest interpretation is to say that the universe is flat. Of course, if we…

Is it possible, or in any way related, that a small but non-zero curvature could be responsible for the accelerated expansion of the universe? I don't know, it's hard to picture. But I'm thinking the idea that you can look at a sphere as a 2 dimensional space that curves and eventually wraps around such that things going opposite directions on its surface eventually can run into each other again. That would probably…

That's a remarkably close guess.

A small non-zero curvature would correspond to a non-zero cosmological constant, which is precisely what seems to be driving the accelerated expansion of the universe (there are other explanations but this is the simplest one).

Re: Why Understanding Space Is So Hard

#73

Post by meric »

CPLX wrote: post #43

Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space.

If one wants to get a sense of how far things are, it's probably more helpful to imagine all bodies besides the moon as being infinitely far away.

At 4km per hour, it takes 11 years of continuous walking to walk the distance between Earth and the Moon; 4252 years to the Sun; 214041 years to Pluto; 1.17 billion years to Alpha Centauri.

Assuming single celled organisms travel very slowly, that means if you have been walking your entire lifetime to Alpha Centauri, and your parents did the same and gave birth to you on their way to Alpha Centauri, and their parents gave birth to them on their way to Alpha Centauri, ancestors all the way back to the first biotic life form, you'd be just about arriving, now.

It does also mean, the sum of all distance traveled by all lifeforms on Earth is longer than the distance between Earth to Alpha Centauri and back by quite a few times, that can likely be measured in the billions.

Re: Why Understanding Space Is So Hard

#74

Post by yaks_hairbrush »

danbruc wrote: post #52
colordrops wrote: post #49

Earlier quoted context omitted.

Angular momentum is an abstract concept, and an emergent property. It doesn't exist inherently in an object.

Spin angular momentum seems to be a pretty intrinsic property of (fundamental) particles. What do you understand as inherent properties of objects? Position? Charge? Mass? Velocity? Energy? Linear momentum? Spin? And why? What if the object is composite? What about quantum physics, e.g. superposition states?

The angular momentum of a spinning bucket of water has approximately nothing to do with the intrinsic angular momentum of the particles, though. Statistically, we'd expect all of the intrinsic spins of the electrons and quarks to cancel out entirely.

Rather, the angular momentum is due to the fact that the straight-line motion of all the atoms on the left side of the bucket is opposite in direction to the straight-line motions of all the atoms on the right side of the bucket. (With respect to the reference frame of the center of gravity of the bucket, etc, etc.)

Re: Why Understanding Space Is So Hard

#75

Post by grondilu »

gkya wrote: post #64
grondilu wrote: post #50

Earlier quoted context omitted.

I've struggled several times to formulate this question properly. I'm not convinced by your formulation. I'll give it an other try. Does space have an existence per se, that is regardless of the matter it contains, or is it just a mathematical framework for the interactions between particles?

This requires a definition of space. For your question to be logical, space should be taken as the thing that is among and around matter. Then on it may be researched physically. Buf if space is taken to mean the thing that exists among and around perceivable matter, then your question becomes obscure, as this means that space is matter, but just not perceivable. And therefore it exists, also without relation.

We know what space is, at least operationally. Or rather space-time. Space is what can be measured with rigid rods. Time is what clocks measure. Einstein painstakingly defined those concepts this way.

Plank's question is more metaphysical : beyond what it means experimentally, does space have a -physical- existence per se, even in a completely empty universe? In other words, is an empty universe different than no universe at all? If not, one way to look at space it is to consider it as a set of abstract rules regarding the possible interactions between particles, those rules being very close to what we call geometry.

Re: Why Understanding Space Is So Hard

#76

Post by danbruc »

yaks_hairbrush wrote: post #74
danbruc wrote: post #52

Earlier quoted context omitted.

Spin angular momentum seems to be a pretty intrinsic property of (fundamental) particles. What do you understand as inherent properties of objects? Position? Charge? Mass? Velocity? Energy? Linear momentum? Spin? And why? What if the object is composite? What about quantum physics, e.g. superposition states?

The angular momentum of a spinning bucket of water has approximately nothing to do with the intrinsic angular momentum of the particles, though. Statistically, we'd expect all of the intrinsic spins of the electrons and quarks to cancel out entirely. Rather, the angular momentum is due to the fact that the straight-line motion of all the atoms on the left side of the bucket is opposite in direction to the straight-li…

They are nonetheless related, if you would align the spins in the water and the (metal) bucket you would make the bucket and/or water spin to conserve the angular momentum. [1] They are surly different but it is not some accident of history that both are called angular momentum, they are really both angular momentum.

[1] https://en.wikipedia.org/wiki/Einstein–de_Haas_effect

Re: Why Understanding Space Is So Hard

#77

Post by scoj »

danbruc wrote: post #71
CPLX wrote: post #43

Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space.

52! is the number of different ways you can arrange a single deck of cards. Let's try to wrap our puny human brains around the magnitude of this number with a fun little theoretical exercise. Start a timer that will count down the number of seconds from 52! to 0. We're going to see how much fun we can have before the timer counts down all the way. Start by picking your favorite spot on the equator. You're going to wa…

Wow. Thank you for sharing this. Amazing to try and wrap your head around this.

Re: Why Understanding Space Is So Hard

#78

Post by yaks_hairbrush »

danbruc wrote: post #76
yaks_hairbrush wrote: post #74

Earlier quoted context omitted.

The angular momentum of a spinning bucket of water has approximately nothing to do with the intrinsic angular momentum of the particles, though. Statistically, we'd expect all of the intrinsic spins of the electrons and quarks to cancel out entirely. Rather, the angular momentum is due to the fact that the straight-line motion of all the atoms on the left side of the bucket is opposite in direction to the straight-li…

They are nonetheless related, if you would align the spins in the water and the (metal) bucket you would make the bucket and/or water spin to conserve the angular momentum. [1] They are surly different but it is not some accident of history that both are called angular momentum, they are really both angular momentum. [1] https://en.wikipedia.org/wiki/Einstein–de_Haas_effect

What is the point you're arguing against? I know perfectly well that conservation of angular momentum is a thing. I know perfectly well that the intrinsic property that we call 'spin' of an electron is really angular momentum. I know that a spinning bucket also has real angular momentum.

So, I'm not sure what you're trying to tell me.

The central point made by colordrops is that angular momentum in a macroscopic object is 100% (accurate to at least ten decimal places) due to synchronicity of linear momenta.

Re: Why Understanding Space Is So Hard

#79

Post by danbruc »

yaks_hairbrush wrote: post #78
danbruc wrote: post #76

Earlier quoted context omitted.

They are nonetheless related, if you would align the spins in the water and the (metal) bucket you would make the bucket and/or water spin to conserve the angular momentum. [1] They are surly different but it is not some accident of history that both are called angular momentum, they are really both angular momentum. [1] https://en.wikipedia.org/wiki/Einstein–de_Haas_effect

What is the point you're arguing against? I know perfectly well that conservation of angular momentum is a thing. I know perfectly well that the intrinsic property that we call 'spin' of an electron is really angular momentum. I know that a spinning bucket also has real angular momentum. So, I'm not sure what you're trying to tell me. The central point made by colordrops is that angular momentum in a macroscopic obje…

What colordrops wrote at least suggest that he thinks that circular motion and angular momentum are not fundamental but can be expressed or understood in terms of linear motion and linear momentum. As far as I can tell today this is not true, they are independent concepts and one can not be fully understood in terms of the other, neither by looking at circular motion as piecewise linear motion nor by looking at linear motion as circular motion about a point infinitely far away. I only brought up spin because it makes the point pretty clear - or maybe not - that angular momentum is a fundamental concept that can not be recast in other terms, especially it is not just the sum of many linear momenta.

Re: Why Understanding Space Is So Hard

#80

Post by [deleted] »

danbruc wrote: post #79
yaks_hairbrush wrote: post #78

Earlier quoted context omitted.

What is the point you're arguing against? I know perfectly well that conservation of angular momentum is a thing. I know perfectly well that the intrinsic property that we call 'spin' of an electron is really angular momentum. I know that a spinning bucket also has real angular momentum. So, I'm not sure what you're trying to tell me. The central point made by colordrops is that angular momentum in a macroscopic obje…

What colordrops wrote at least suggest that he thinks that circular motion and angular momentum are not fundamental but can be expressed or understood in terms of linear motion and linear momentum. As far as I can tell today this is not true, they are independent concepts and one can not be fully understood in terms of the other, neither by looking at circular motion as piecewise linear motion nor by looking at linea…

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