Ask a physicist anything. (7)

[Chalnoth]

Good, I don't have to imagine fractal spacetime then!

Speaking of fractals, can a real-world object be a true fractal? Since physical objects have finite sizes, I would think that a fractal is always just an approximation.

Though, that's the same reasoning that says we can't have a perfect circle, so I'm not sure it's as profound as it seemed at first glance

Right, I'm pretty sure this is exactly correct

 

[Naraoia]

Maybe there really is a fundamental particle far below quarks and gluons, which has a really real shape - but it's a 3D Koch snowflake, which (somehow) gives rise to the quantum effects we see at the nano scale, and in turn the classical effects at the macro scale. So who knows, maybe it really is squiggly edges all the way down...

Spooky!

I like those sphereflakes.

 

[Lillen]

How can universe expand when no new energy is added to it?

 

[Chalnoth]

How can universe expand when no new energy is added to it?

Why would you think expansion requires energy?

 

[Lillen]

Otherwise we would only have one star...

 

[Selmak]

What is beyond the light horizon? More of the same?

 

[Chalnoth]

Otherwise we would only have one star...

You didn't actually explain your reasoning. Why would we have one star?

 

[Chalnoth]

What is beyond the light horizon? More of the same?

Well, the fact that our universe does not change, on average, as far as we can see strongly suggests that there is more of the same, at least for some significant distance. Exactly how far, we don't know.

 

[Selmak]

Well, the fact that our universe does not change, on average, as far as we can see strongly suggests that there is more of the same, at least for some significant distance. Exactly how far, we don't know.

If the universe is expanding outward from a single point, why isn't there a vast empty void in the center?

 

[Chalnoth]

If the universe is expanding outward from a single point, why isn't there a vast empty void in the center?

It's not expanding from a single point. It's expanding at every point. Everywhere in the universe, the average distance between galaxies is increasing. Objects are moving away from every point. There is no center.

 

[Selmak]

It's not expanding from a single point. It's expanding at every point. Everywhere in the universe, the average distance between galaxies is increasing. Objects are moving away from every point. There is no center.

Please expand on this - I'm not following. It's my understanding that the universe arose from a singularity that began expanding outward about 13.7 billion years ago. Why then isn't the material universe like the skin of a balloon? I'm probably not explaining myself well here. I appreciate your patience.

 

[Chalnoth]

Please expand on this - I'm not following. It's my understanding that the universe arose from a singularity that began expanding outward about 13.7 billion years ago. Why then isn't the material universe like the skin of a balloon? I'm probably not explaining myself well here. I appreciate your patience.

The singularity is a misnomer. It didn't happen. It can't have happened because it's nonsensical. The existence of that singularity in our equations means that our equations aren't correct that far back in time.

The way to understand our very early universe is basically that it was an almost perfectly-uniform, unbelievably hot soup. It was like this everywhere. The expansion means that this hot soup was getting less dense and cooler over time. Our universe has gotten much bigger since then, so that now it is full of mostly-empty space, with hundreds of billions of galaxies littered here and there.

 

[Naraoia]

Why would you think expansion requires energy?

Wait, it doesn't?

 

[Chalnoth]

Wait, it doesn't?

Nope. Energy isn't conserved in an expanding universe. If you want a detailed description of the issue, check this out:
Is Energy Conserved in General Relativity?

The super short version is simply that there is no unique way to define overall energy in General Relativity. And what you can't define, you can't conserve.

But even more simply, an object in motion stays in motion unless acted upon by an external force. In other words, once the expansion gets started, it continues going on its own. There is no need to input additional energy to keep the expansion going.

 

[Selmak]

How long will it be until the heat death of the universe? Assuming the human race survives for the lifespan of the universe, can we theoretically delay the heat death of at least a portion of it to preserve our own existence somewhat longer?

 

[Chalnoth]

How long will it be until the heat death of the universe?

A long, long time. Wikipedia has a good breakdown:
Future of an expanding universe - Wikipedia, the free encyclopedia

Assuming the human race survives for the lifespan of the universe, can we theoretically delay the heat death of at least a portion of it to preserve our own existence somewhat longer?

Somewhat. If you read the above link, one of the critical points will be planets being flung from their orbits over time. A sufficiently advanced civilization might be able to prevent this (though it would be one hell of an undertaking).

But regardless, human civilization is only around 10,000 years old. New stars will still keep being made for another 100,000,000,000,000 years. That is ten billion times the age of human civilization.

In other words, if we can survive ourselves for the next few centuries, and can survive our star going red giant in a few billion years, our species will likely have a very, very long life ahead of it. I don't see anything sad about living such an unbelievably long time.

 

[Naraoia]

Nope. Energy isn't conserved in an expanding universe. If you want a detailed description of the issue, check this out:
Is Energy Conserved in General Relativity?

The super short version is simply that there is no unique way to define overall energy in General Relativity. And what you can't define, you can't conserve.

But even more simply, an object in motion stays in motion unless acted upon by an external force. In other words, once the expansion gets started, it continues going on its own. There is no need to input additional energy to keep the expansion going.

The universe somehow gets weirder every time I talk to a physicist!

(I just wish I knew what the heck a covariant derivative was... the fact that I'd have to look up like every other word in the Wikipedia article on them suggests that it's quite far beyond the maths I [used to] know )

Hmm. Wait, why can't you simply add vectors in curved spacetimes? I have a feeling that this also runs into maths I never even knew existed, but I'll try not to be too dense!

 

[Chalnoth]

Hmm. Wait, why can't you simply add vectors in curved spacetimes?

Well, you can, as long as both vectors are at the same point. That is, you can find the relative velocity between two objects only as they are passing one another. Once the objects are far away, you can no longer simply subtract their velocities: the curvature of space-time in between the objects makes the definition of vector subtraction ambiguous.

So it shouldn't be a surprise that if you only examine what goes on at a single point, you get energy conservation just fine. It's only when you start dealing with large regions that this starts to break down.

Why does not being at the same place matter? Well, this comes down to the curvature. There is a way in General Relativity to move a vector from one place to another, for example. This is called parallel transport. What parallel transport means is that you move the vector along some path between two points, keeping it parallel to itself as it moves. Sounds reasonable, right?

Well, here's the kicker: in curved space-times, the vector you get as a result depends upon the path you take! What this means is that ultimately, any sort of vector subtraction you try to do between points far away will depend upon how you define your terms.

Edit:
Just to drive the point home, I thought I'd take a simple example. Imagine, if you will, a vector on the surface of the Earth. Let's start out with this vector at the North Pole, and the vector points along the surface, let's say towards 0 degrees longitude. What happens if we parallel transport the vector along the 0 degrees longitude line to the equator? Well, the vector will always point along the surface, pointing in the direction it's moving, so that when the vector reaches the equator, it will be pointing due south.

Now let's try another path. Instead of moving this vector along 0 degrees longitude (which goes through England), let's move it along 90 degrees longitude (which goes through the US). Now the vector is not pointing along the direction of motion, but perpendicular to it. Its direction along that motion, then, will always be due east, up until it reaches the equator. Then, if we move the vector along the equator back to 0 degrees longitude, it will still be pointing due east.

Because of the curvature of the Earth, then, there is no way to say unambiguously how to do vector subtraction between two different places on the surface of the Earth.

 

[Selmak]

I heard in passing something about the expansion of the universe being observed to be accelerating. If this is the case, will we reach relativistic velocities in the future that will effectively cease the passage of time from our perspective?

 

[Chalnoth]

I heard in passing something about the expansion of the universe observed to be accelerating. If this is the case, will we reach relativistic velocities in the future that will effectively cease the passage of time from our perspective?

Well, no, it doesn't work that way. From our perspective, we will always be (nearly) stationary with respect to the expansion. So will every other galaxy, from their perspective.

We do, however, see other galaxies, galaxies with large redshifts, as being time-dilated. In fact, the redshift itself is the time dilation, and we see some galaxies at redshifts corresponding to time dilation factors of nearly 10. That is, from our perspective, we see time moving at around 1/10th the speed on those far-away galaxies (if we could see a clock that far away, for example, it would take nearly 10 minutes to see the minute hand on a clock on those galaxies tick once).

But this is the case whether or not the expansion is accelerating. What the accelerating expansion means is that there are many objects which we can see today that light emitted today from us will never reach. Similarly, we will never see those galaxies age past a certain age, the age they passed our horizon.