Dark Energy in Relation to Spacetime

[physicsquestion11]

Hello.
I'm not sure if this is an A level thread however I'll just post it here.
I have a question that regards dark energy in relation to space time.

I've learned that dark energy only affects space and not time. However I've also learned that space and time are intrinsically intertwined as shown through general relativity.
And so how can dark energy only affect space and not time? Is the reason unknown, or is there some type of property within dark energy that makes it so it can't affect time?

Regards,
Daniel

 

[PeterDonis]

I'm not sure if this is an A level thread

It's not. An A level thread assumes that you have the background knowledge of a physics graduate student. I've changed the level to B.

I've learned that dark energy only affects space and not time.

Where did you learn that? Can you give a reference? Your reasoning about space and time being intrinsically connected is correct; so anything that affects space must also affect time. (A better way of putting it would be that "space" and "time" depend on your choice of coordinates, so even if something only affects "space" in one coordinate system, you can make it affect "time" as well by changing coordinates. But no actual physics can depend on your choice of coordinates.) So it looks like you have misinterpreted something in whatever source you got the quoted statement about dark energy from. But we would have to know the source to figure out what you misinterpreted.

 

[physicsquestion11]

It's not. An A level thread assumes that you have the background knowledge of a physics graduate student. I've changed the level to B.

Ah, my bad. The reason I put it in level A is because I wasn't sure if it would be taught prior to graduate class.

Where did you learn that? Can you give a reference?

So I created this thread off a memory of a previous discussion. https://www.physicsforums.com/threads/what-does-expand-space-or-spacetime.845828/

It turns out that the actual question is not pertaining to dark energy but rather the expansion. However the question still remains for me: why does space expand and not spacetime when they're fundamentally connected?

 

[Orodruin]

It turns out that the actual question is not pertaining to dark energy but rather the expansion. However the question still remains for me: why does space expand and not spacetime when they're fundamentally connected?

This is again a question of definitions. Note that something expanding requires a time dependence. Spacetime is not time dependent, time itself is a part of it. There is a standard way of writing down time and space coordinates in cosmology. If you do this, you can look at what space looks like for different times. You would find that it is larger for later times and this is what expansion is about.

 

[physicsquestion11]

This is again a question of definitions. Note that something expanding requires a time dependence. Spacetime is not time dependent, time itself is a part of it. There is a standard way of writing down time and space coordinates in cosmology. If you do this, you can look at what space looks like for different times. You would find that it is larger for later times and this is what expansion is about.

That's really interesting.
So the amount of time that has occurred is correlated with the expansion of space and vice versa?
With increased time, space must also increase as well? Also, if what I said is true, would that mean that due to space accelerating recently time is accelerating as well? Perhaps I'm misinterpretation your answer or maybe taking my intuition concerning the subject too far.

 

[Orodruin]

With increased time, space must also increase as well?

It is unclear what you mean by this. This is the problem of phrasing scientific statements in language other than mathematics.

Also, if what I said is true, would that mean that due to space accelerating recently time is accelerating as well?

No. In fact the phrase "accelerating time" is a contradiction in terms. By definition, acceleration is how fast a rate of change changes with "fast" having an intrinsic referral to time. Time relates directly and linearly to time and therefore cannot accelerate. You can have different other concepts such as time dilation, but here we are talking about cosmological time, which makes it well defined.

Perhaps I'm misinterpretation your answer or maybe taking my intuition concerning the subject too far.

This is a problem. You simply cannot use your intuition unless you have built that intuition by deeply studying the subject matter (and I do not mean reading about it in popular scientific articles, I mean really studied the subject in terms of its mathematical structure). Intuition is built by familiarity and unless you study the subject matter deeply you will not have any. Our intuition for physical processes occurring in our surroundings builds on years of being exposed to them.

 

[physicsquestion11]

It is unclear what you mean by this. This is the problem of phrasing scientific statements in language other than mathematics.

Thanks for the response. I should have been more clear in what I said, as I formulated the question rather strangely.
Here you said that "You would find that [the space] is larger for later times and this is what expansion is about".
From this sentence I derived my understanding that the amount of expansion in space is correlated with the amount of time that has occurred.
My further questions were then predicated off of that.

I admit that I'm not very familiar with the subject and I appreciate the help. :)

 

[Orodruin]

From this sentence I derived my understanding that the amount of expansion in space is correlated with the amount of time that has occurred.

A better way of putting it is that the size of space is correlated with the amount of time that has passed. It is unclear how you go from here to inferring that time somehow would expand.

 

[PeterDonis]

why does space expand and not spacetime

If you read Orodruin's post #4 carefully, you will see that he says space is expanding in a particular set of coordinates. And if you read my post #2 again, you will see that I said that "space" and "time" depend on your choice of coordinates. (I also said that no actual physics can depend on your choice of coordinates. The particular coordinates Orodruin referred to are used because they are very convenient for cosmology, not because they are required by the physics.)

Also, it doesn't make sense to say that spacetime "expands". Spacetime just is; it's a 4-dimensional geometric object that describes the entire history of the universe. "Expanding space" is just a term we use to describe a particular type of geometry of spacetime; we use it because the "space" defined by the coordinates that are most convenient for cosmology is expanding in those coordinates.

So we say that space is expanding but not spacetime (and not time) for two reasons: first, because it reflects the description given by the coordinates we find most convenient for cosmology; and second, because the concepts of time or spacetime expanding don't make sense.

 

[physicsquestion11]

The size of space is correlated with the amount of time that has passed.

I want to make sure I understand this 100%. If this is true then wouldn't the following list also be true?

The size of space and the amount of time that has passed are correlated, so therefore:

The size of space must be correlated with the amount of time that has passed.
The amount of time that has passed must be correlated with the size of space.
As long as time progresses, the size of space must also progress.
As long as the size of space progresses, the amount of time must progress.

 

[physicsquestion11]

It is unclear how you go from here to inferring that time somehow would expand.

If space and time are correlated, and if space started to accelerate in a rapid manner wouldn't this mean that time must do the same? Or maybe the constant that the size of space increases with time must be getting larger.

I'm really sorry if I'm just spurring rubbish out of my mouth.
Thanks again. :)

 

[phinds]

I want to make sure I understand this 100%. If this is true then wouldn't the following list also be true?

The size of space and the amount of time that has passed are correlated, so therefore:

The size of space must be correlated with the amount of time that has passed.

Well, not necessarily, since the "size" of space could be infinite which case it has always been infinite and always will be infinite. The amount of space encompassing a square cornered by two galaxies far removed from each other (so as not to be gravitationally bound) will increase over time.

The amount of time that has passed must be correlated with the size of space.

as has already been pointed out, if the amount of space is increasing that of necessity involved an increase in time.

As long as time progresses, the size of space must also progress.

Not must, but it does in the universe we live in. It didn't have to, if by "progress" you mean "increase". Before the discovery of dark energy and the accelerated expansion, the Big Crunch scenario was considered feasible.

As long as the size of space progresses, the amount of time must progress.

Again, you're getting in tautologies with words here, if by "progresses" you mean "increased in the universe we live in".

 

[PeterDonis]

If space and time are correlated, and if space started to accelerate in a rapid manner wouldn't this mean that time must do the same?

No. What "space started to accelerate" means, roughly speaking, is "the rate of expansion of space started to increase with time". "Time" here is the fixed reference that is used to determine the "rate of space expansion". (Also bear in mind that all of this assumes that we are using the standard cosmological coordinates; i.e., it's coordinate-dependent.)

Basically what you are running into here is that the statement "space and time are correlated" doesn't mean what you think it means. It's not a fundamental statement about how the spacetime of our universe works. It's just a side effect. To really understand the fundamentals, you need to take the time to understand the actual math--the actual model, based on general relativity, that cosmologists use to understand the large-scale behavior and history of the universe.

The best starting reference I can give is Ned Wright's cosmology faq and tutorial:

http://www.astro.ucla.edu/~wright/cosmolog.htm

Working through these may help you understand at least the basics.