Is Expansion the Same as Contraction?

[theoretical symmetry]

How do you tell the difference of expanding outwards and contracting inwards?

Part of my intuition tells me that it would be impossible to tell the difference.

If you are on the natural numbers heading from zero to infinity I might say that is expanding outwards.

So if you are sitting at zero and moving to negative infinity then that would seem like contracting inwards. However you would leave the positive numbers behind and have negative numbers ahead but since you are moving forward it would seem natural to label those numbers as positive and the others as negative.

So the forward arrow of time would imply that the numbers covered would always appear as the natural numbers.

The larger part of my intuition tells me that I could be way far off and not even know it without checking with PF.

Thoughts?

 

[phinds]

How do you tell the difference of expanding outwards and contracting inwards?

Expansion creates red shift (which we observer), contraction would create blue shift (which we do not observe), and that is just one of the ways that we know the universe is expanding.

 

[fresh_42]

Your question is hard to answer. Expansion and contraction of materials like metals is classically a matter of temperature. But as you posted in the relativity theory forum, I suspect it is about time dilation and length contraction at relativistic speeds. But this cannot be explained by or even compared to the distribution of numbers on the number line, no matter which way you "walk" or "how far".

It is due to different perspectives which depend on the rest frame (coordinate system) you observe an object in motion. Have you tried to understand the Wikipedia entry about it?

In any case, we need a more specified question for an answer. Otherwise it would lead to a lecture about special relativity, which cannot be done here. May I ask you about your background, in order to provide an appropriate link to what can be read about it?

 

[theoretical symmetry]

I was leaning more towards the notion that a red shift would be observed even in a contacting universe because from within that reference frame everything would appear to be expanding.

 

[theoretical symmetry]

Your question is hard to answer. Expansion and contraction of materials like metals is classically a matter of temperature. But as you posted in the relativity theory forum, I suspect it is about time dilation and length contraction at relativistic speeds. But this cannot be explained by or even compared to the distribution of numbers on the number line, no matter which way you "walk" or "how far".

It is due to different perspectives which depend on the rest frame (coordinate system) you observe an object in motion. Have you tried to understand the Wikipedia entry about it?

In any case, we need a more specified question for an answer. Otherwise it would lead to a lecture about special relativity, which cannot be done here. May I ask you about your background, in order to provide an appropriate link to what can be read about it?

Undergraduate physics / mathematics

 

[theoretical symmetry]

I was thinking of it on a numberline as a bunch of particles moving at various speeds. Everything starts off at zero and tends to infinity Pick a particle and measure other particles since they are all moving in the same direction it will always seem like an expansion even if everything tends to negative infinity.

 

[fresh_42]

I was thinking of it on a numberline as a bunch of particles moving at various speeds. Everything starts off at zero and tends to infinity Pick a particle and measure other particles since they are all moving in the same direction it will always seem like an expansion even if everything tends to negative infinity.

This sounds a bit like the light clock, which is explained in the article I linked to. You will have to determine a rest frame, in which you observe the particles, e.g. not moving at $0$ or co-moving with one particle. But what should expand or contract? Particles don't have a size, but their specific time is different from yours. This experiment might be interesting in the context: http://web.mit.edu/8.13/www/JLExperiments/JLExp14.pdf

 

[theoretical symmetry]

Thanks. I am going to read up on the info provided and will return with any more questions or perhaps a rephrasing of the initial question to better assist you in answering it. I appreciate all the responses and links.

 

[phinds]

I was leaning more towards the notion that a red shift would be observed even in a contacting universe because from within that reference frame everything would appear to be expanding.

OK, you've got me completely flummoxed with that statement. I can't imagine how you arrive at that conclusion since it seems to me to be self-contradictory. What am I missing?

 

[Dale]

I was leaning more towards the notion that a red shift would be observed even in a contacting universe

No, that is essentially the definition of an expanding universe.

 

[PAllen]

I was leaning more towards the notion that a red shift would be observed even in a contacting universe because from within that reference frame everything would appear to be expanding.

No, this is just wrong. FLRW family of cosmological GR solutions allows for contracting universes as well as expanding. The former have blue shift increasing with distance for comoving sources, while latter have redshift.

 

[PeterDonis]

How do you tell the difference of expanding outwards and contracting inwards?

Take out the words "outwards" and "inwards"; they are redundant. Then ask the question again; is the answer now obvious?

 

[theoretical symmetry]

OK, you've got me completely flummoxed with that statement. I can't imagine how you arrive at that conclusion since it seems to me to be self-contradictory. What am I missing?

T-Duality? I figured (wrongly) that if this were true then we wouldn't know if our universe has a very large radius or a very small one. So universe expanding for 46 light years to it's current radius R should be the same size as if it was contracting to 1/R. I thought would always appear expanding because the difference from 1 increases with time.

 

[phinds]

T-Duality? I figured (wrongly) that if this were true then we wouldn't know if our universe has a very large radius or a very small one. So universe expanding for 46 light years to it's current radius R should be the same size as if it was contracting to 1/R. I thought would always appear expanding because the difference from 1 increases with time.

I have no idea what any of what you just said means.

 

[theoretical symmetry]

I have no idea what any of what you just said means.

From wikipedia "In theoretical physics, T-duality is an equivalence of two physical theories, which may be either quantum field theories or string theories. In the simplest example of this relationship, one of the theories describes strings propagating in an imaginary spacetime shaped like a circle of some radius R, while the other theory describes strings propagating on a spacetime shaped like a circle of radius proportional to 1/R}. The two theories are equivalent in the sense that all observable quantities in one description are identified with quantities in the dual description."

 

[phinds]

From wikipedia "In theoretical physics, T-duality is an equivalence of two physical theories, which may be either quantum field theories or string theories. In the simplest example of this relationship, one of the theories describes strings propagating in an imaginary spacetime shaped like a circle of some radius R, while the other theory describes strings propagating on a spacetime shaped like a circle of radius proportional to 1/R}. The two theories are equivalent in the sense that all observable quantities in one description are identified with quantities in the dual description."

Ah. Well that explains "T-duality". Thanks. I still have no idea what that has to do with the universe expanding and not contracting.

 

[Bandersnatch]

If you are on the natural numbers heading from zero to infinity I might say that is expanding outwards.

So if you are sitting at zero and moving to negative infinity then that would seem like contracting inwards. However you would leave the positive numbers behind and have negative numbers ahead but since you are moving forward it would seem natural to label those numbers as positive and the others as negative.

I was thinking of it on a numberline as a bunch of particles moving at various speeds. Everything starts off at zero and tends to infinity Pick a particle and measure other particles since they are all moving in the same direction it will always seem like an expansion even if everything tends to negative infinity.

What you describe as contraction in your example with the number line isn't contraction - it's expansion. Expansion is when the distance between every two arbitrarily chosen points increases with time - it is not when their coordinates become more negative.
If you have a coordinate system in 1-dimensional space (line), where you're at the origin, and you look at some particle sitting to the left (in the negatives), and then look at it later, you get expansion when the distance will have increased. You get contraction when the distance will have decreased.

 

[Herman Trivilino]

So universe expanding for 46 light years to it's current radius R should be the same size as if it was contracting to 1/R.

You cannot have a radius of $\frac{1}{R}$. It doesn't make sense to speak of such a thing in any context.

Now, it does make sense to speak of a contracting universe, but as has been pointed out several times in this thread, all observations indicate that the universe is expanding, not contracting. In you original post you asked it it were possible to tell the difference and we've told that it is possible, and that it has been done.

Adding the adjectives inward and outward do one of two things: add a redundancy or produce nonsense. Here are the four relevant examples.

An outward expansion (outward is redundant and therefore can be removed without altering the meaning of the phrase).
An inward expansion (nonsense because the inward direction is opposite to the direction of expansion).
An inward contraction (inward is redundant and therefore can be removed without altering the meaning of the phrase).
An outward contraction (nonsense because the outward direction is opposite to the direction of contraction).

 

[russ_watters]

How do you tell the difference of expanding outwards and contracting inwards?

Part of my intuition tells me that it would be impossible to tell the difference.

I feel like you've tied yourself in some sort of logical knot and can't get out or fell down a speculative rabbit hole and can't see how you got here. Please, take a step back, find a balloon, blow it up. That's expansion. Let it go. That's contraction. There is no possible way you could mistake one for the other.

So universe expanding for 46 light years to it's current radius R should be the same size as if it was contracting to 1/R. I thought would always appear expanding because the difference from 1 increases with time.

You've [almost] constructed an equation: R=1/R. Now use it! Quite clearly, it can only be valid for R=1. For increasing (expanding) numbers, you have:
2=1/2=False!
3=1/3=False!
4=1/4=False!
Etc.

Clearly, expansion and contraction are not equivalent.

If you are on the natural numbers heading from zero to infinity I might say that is expanding outwards.

So if you are sitting at zero and moving to negative infinity then that would seem like contracting inwards.

Well, there are two easy ways to test this:
1. Plug some negative numbers into your equation and let me know if it produces a valid result.
2. Draw, with your mind, a set of X,Y,Z axes through the center of your balloon and then blow up the balloon. What happens on the negative side of the axes?