How Does the Universe Expand According to Physics?

[Visigoth]

Most people, Physicists or otherwise, understand that the Universe is expanding. But I'm somewhat perplexed as to how. To "expand", by classical physics, means for an object to extend it's reach in one or all of the 3 dimensions of space, i.e. getting wider, taller, longer, etc. Therefore, space is the medium. But if spacetime itself can expand, what is the medium for this expansion?

 

[Nabeshin]

The expansion refers to the fact that there is a factor which changes with time which is used to measure dimensions. So, let's look at the spatial part of the flat FRW metric:
$$ds^2=a^2(t)\left[dx^2+dy^2+dz^2\right]$$
This is basically just a differential form of the Pythagorean theorem, but with this extra constant factor out front of a(t). Let a=1 now, and let's just say we have a ruler along the x-axis which has length 1. Since a is a function of time, at some later time perhaps a=2, and now the same ruler (same dx! this remains unchanged!) is now 4 units long! This is the basic idea of the concept of expansion, so you can see that it doesn't require the 3 spatial dimensions to expand into anything.

 

[Visigoth]

The expansion refers to the fact that there is a factor which changes with time which is used to measure dimensions. So, let's look at the spatial part of the flat FRW metric:
$$ds^2=a^2(t)\left[dx^2+dy^2+dz^2\right]$$
This is basically just a differential form of the Pythagorean theorem, but with this extra constant factor out front of a(t). Let a=1 now, and let's just say we have a ruler along the x-axis which has length 1. Since a is a function of time, at some later time perhaps a=2, and now the same ruler (same dx! this remains unchanged!) is now 4 units long! This is the basic idea of the concept of expansion, so you can see that it doesn't require the 3 spatial dimensions to expand into anything.

Okay, so according to the metric, there is some factor (which I'm assuming is unknown?) innate to time that causes the "expansion". I'm still struggling to understand why this phenomenon exists only for space itself, and not things which are a part of spacetime. I'm assuming this is a conceptual misunderstanding?

 

[Visigoth]

Or, and I suppose this might answer my previous question, by space expanding, does it mean everything, all matter is also "expanding"? We simply can't notice it due to frames of reference and the fact that all space expands at the same rate?

 

[Nabeshin]

Okay, so according to the metric, there is some factor (which I'm assuming is unknown?) innate to time that causes the "expansion".

Actually, it's not unknown. It can be solved for from some well known equations known as the http://en.wikipedia.org/wiki/Friedmann_equations" .

Or, and I suppose this might answer my previous question, by space expanding, does it mean everything, all matter is also "expanding"? We simply can't notice it due to frames of reference and the fact that all space expands at the same rate?

Were there no forces between objects, yes everything would expand. As it stands, however, the forces in a object, say a planet, act to hold the object together. Now, under most cirumstances, the forces binding an object together are exponentially more powerful than the "expansive force" created by the changing scale factor (the a(t) function is known as the scale factor). So while the distance between galaxy clusters might expand (gravity binding is less than the 'expansive force'), the distance between constituent parts of the Earth will not.

Does that answer your question? I'm having a tough time pinning down precisely what it is and if I can answer it for you.

 

[Chalnoth]

Were there no forces between objects, yes everything would expand.

Well, sort of. If the matter in the universe was distributed perfectly uniformly, this would be the case: everything would expand. However, the matter is not distributed perfectly uniformly, and the same gravity that determines how the expansion progresses also makes it so that bound objects (like galaxies and whatnot) do not expand.

 

[Visigoth]

Okay, this all makes sense now. I've looked over friedmann's equations and it's simpler to understand now.

One last question, since we're on the topic, given that the Universe expands as the metric predicts it, why is dark energy attributed to the expansion of the universe? Or is Dark Energy only theorized to account for the increasing rate of expansion?

 

[Calimero]

Or is Dark Energy only theorized to account for the increasing rate of expansion?

Correct.

 

[JayKosta]

(Hello everyone, I am new to this forum...)

Does the 'expansion' produce actual increased velocity of the mass that is affected?

Does the 'theory of relativity' pertain to this increased 'expansion' velocity, mass, and energy needed to achieve increased velocity?

Jay Kosta
Endwell NY USA

 

[Jack21222]

(Hello everyone, I am new to this forum...)

Does the 'expansion' produce actual increased velocity of the mass that is affected?

Does the 'theory of relativity' pertain to this increased 'expansion' velocity, mass, and energy needed to achieve increased velocity?

Jay Kosta
Endwell NY USA

The expansion doesn't have a direction, so no velocity. At least, that's my amateur understanding of it.

 

[Nabeshin]

Okay, this all makes sense now. I've looked over friedmann's equations and it's simpler to understand now.

One last question, since we're on the topic, given that the Universe expands as the metric predicts it, why is dark energy attributed to the expansion of the universe? Or is Dark Energy only theorized to account for the increasing rate of expansion?

Ok, in the wiki link I gave for the friedmann equations you see the section titled "Density Parameter"? Basically we can predict or measure the various omega values for mass, radiation (and I guess curvature). But when we put in only what we can observe, the omega values are FAR too small to give rise to the universe we currently observe (predictions are absurd). So, from galactic dynamics and other such, we can bump up the matter omega by considering dark matter, which helps but does not solve the problem completely. And with the discovery of an "accelerating expansion" in the late 90's, the only option left was to tweak the omega lambda, which is the so-called dark energy term.

 

[everymanjack]

Where do the data points showing accelerating expansion come from? From redshift in light from the past (i.e., from far away)? If so, why isn't the expansion in the past? Or is redshift more pronounced in more recent (closer) data?

 

[Chalnoth]

Where do the data points showing accelerating expansion come from? From redshift in light from the past (i.e., from far away)? If so, why isn't the expansion in the past? Or is redshift more pronounced in more recent (closer) data?

The first bit of data came from supernovae: far-away supernovae were dimmer than we expected them to be. These data have since been confirmed by measures of how length scales change with redshift through baryon acoustic oscillation and CMB measurements in particular.

 

[everymanjack]

The first bit of data came from supernovae: far-away supernovae were dimmer than we expected them to be. These data have since been confirmed by measures of how length scales change with redshift through baryon acoustic oscillation and CMB measurements in particular.

I get the part about type 1a supernovae working as standard candles, and about redshift showing light's recession. What I don't get is the temporal location of expansion in the now ("is expanding") as opposed to the past. But then, I generally have a hard time grasping the relationship between spatial expansion and time. Is it just me, or is it hard to explain? I also don't truly understand the CMB, esp. the uniformity of its temperature, but that's another thread.

 

[Chalnoth]

I get the part about type 1a supernovae working as standard candles, and about redshift showing light's recession. What I don't get is the temporal location of expansion in the now ("is expanding") as opposed to the past. But then, I generally have a hard time grasping the relationship between spatial expansion and time. Is it just me, or is it hard to explain? I also don't truly understand the CMB, esp. the uniformity of its temperature, but that's another thread.

Well, it's just that light takes time to get places. So when we look far away, we're looking back in time. The mathematical details get a bit complex in a universe that expands with time, and crucially whose expansion changes with time. But the basic idea is that we look at how the universe has expanded in time by looking at the relationship between distance and redshift in different places.

 

[everymanjack]

As I understand it, expansion and time are sort of the same thing: a galaxy that's a billion lightyears away now will be two billion lightyears away in a billion years. Also, it makes sense that the relationship between time and distance is the same no matter what galaxy you're in. All galaxies see other galaxies recede as time passes. As you say, the changes in expansion with time are crucial. That's just the part I don't understand. Like, take the acceleration of the expansion going on now. I get it that if we observe more redshift in light from galaxies that are really far away it's reasonable to assume that they are receding faster. But how can we tell which end the accelleration is at?

 

[Chalnoth]

I get it that if we observe more redshift in light from galaxies that are really far away it's reasonable to assume that they are receding faster. But how can we tell which end the accelleration is at?

Which end? What do you mean? The expansion is uniform in space. The acceleration we're talking about isn't an acceleration of individual objects, but rather that the first derivative of the scale factor is increasing with time.