Properties of Expansion

[TakenItSeriously]

If the Hubble Law is ultimately based on this fact:

Galaxies that are farther away have a faster regression speed.

 

And from that we conclude:

The expansion of the universe accelerates as it grows.

 

 

Then what about the statement:

Galaxies that exist later in time have a slower regression speed.

 

Symmetry should tell us that:

The expansion of the universe decelerates as it ages.

 

Both statements should be true but how does the expansion of the Universe do both?

accelerate with distance

decelerate with time

 

Does anyone else see a second order Lorentz transform here?

Just puttin it out there.

 

 

Edit to clarify:

Since we found expansion accelerating over distance (dv/dx) is increasing.

 

If we looked at the problem differently and noted that.

 

Galaxies we observe later in time have a lower regression speed.

 

Since every distance measured can also be seen as a delta time from proper time as in a galaxy 10Billion ly away is also 10Billion years in the past.

 

Then by Swapping distance with time and modifying the equations, we can then solve for expansion accelerating over time (dv/dt)

 

It seems like we would get the opposite result due to a spacetime axis symmetry..

Edited February 19, 2016 by TakenItSeriously

[Mordred]

It's in how your defining the system.

 

There is a common misconception with pop media expansion rate they don't tell the full story properly.

 

First off the rate of expansion today per Mpc is defined by Hubbles constant. Hubbles constant isn't constant. The value is only the same everywhere in the universe at the same time. (It's an historical term were stuck with, it's more accurately Hubbles parameter)

 

Second recessive velocity isn't a real velocity.... its classed as an apparent velocity. The galaxies gain no inertia.

 

Now as to your question.

 

If you measure expansion as per Hubbles parameter km/s/Mpc the rate of expansion is slowing down. Since the CMB it's slowed down considerably.

 

If however you measure expansion via the radius of the observable universe it's accelerating. This is because of the gained Mpc.

Let's say expansion growth is 100% increase for each Mpc.

 

measure radius.

 

1

2

4

8

16.

 

But the rate per Mpc is still 100%.

 

 

(Basically the two terms are due to seperation distance between measurement a and b.)

Edited February 18, 2016 by Mordred

[Strange]

If the Hubble Law is ultimately based on this fact:

Galaxies that are farther away have a faster regression speed.

 

And from that we conclude:

The expansion of the universe accelerates as it grows.

 

No. The increasing speed with distance is due to a constant rate of expansion. It is just simple arithmetic.

 

Consider a number of galaxies separated by the same distance (far enough apart that the expansion of space is significant and the same between all of them).

 

At time 0, they are 1 unit apart:

A.B.C.D.E.F

 

After some time they are 2 units apart:

A..B..C..D..E..F

 

After the same time again, they are 3 units apart:

A...B...C...D...E...F

 

And so on:

A....B....C....D....E....F

 

Now, if we look at the distance between B and C, for example, it increases by 1 at every time step. But the distance between B and D increases by 2 at every step. So the distance between B and D is increasing twice as fast as the distance between B and C; i.e. the speed of separation is twice as great.

 

Choose any pairs of galaxies and you will see that apparent the speed of separation is proportional to the distance between them. Take two objects far enough apart and the speed of separation will be greater than the sped of light. (But that is OK, because the speed of light limit is a local thing, whereas these objects are in different frames of reference.)

[TakenItSeriously]

I'm afraid I may not have been very clear in my OP.

 

to clarify:

Since we found expansion accelerating over distance (dv/dx) is increasing.

 

If we looked at the problem differently and noted that.

 

Galaxies we observe later in time have a lower regression speed.

 

Since every distance measured can also be seen as a delta time from proper time as in a galaxy 10Billion ly away is also 10Billion years in the past.

 

Then by Swapping distance with time and modifying the equations, we can then solve for expansion accelerating over time (dv/dt)

 

It seems like we would get the opposite result due to a spacetime axis symmetry.

 

I'll edit my OP to add the clarification.

 

Edit to add again:

Since I don't know where to find the data used, I can't check it myself. If anyone could direct me to where the data was published. assuming it's in the public domain, I'd really appreciate it if they could provide a link.

 

Sorry for all the edits.

Edited February 19, 2016 by TakenItSeriously

[Strange]

I'm afraid I may not have been very clear in my OP.

 

I don't think you understand. You seem to be mixing up a steady rate of expansion, which necessarily results in the speed of separation being proportional to distance, and accelerating expansion.

 

 

Since we found expansion accelerating over distance (dv/dx) is increasing.

 

That does not represent acceleration. That is a constant rate of expansion.

[TakenItSeriously]

I don't think you understand. You seem to be mixing up a steady rate of expansion, which necessarily results in the speed of separation being proportional to distance, and accelerating expansion.

 

It's definitely possible, I'm still struggling to find an article that explains the math in a simplistic way without getting too involved with the details behind all the measurements that include multiple measurements for distance.

 

I don't think that independent galaxies that show a trend for velocities increasing/decreasing with time or distance proves acceleration. I do think the trend is highly suggestive that it's true, especially considering the timeframes axis symmetry that is involved.

 

How the solution for "proving", acceleration was found I'm only guessing at at this point as I haven't seen anything that verifies the method used yet.

 

My guess is that the solution involves using the Hubble law with the Hubble constant and Lookback distance then use the scale factor with redshift to find projected velocities at proper time but I don't know this for a fact. It's just that all the variables are there to provide v₀. As you pointed out this only creates the boundary conditions that could show an average acceleration/deceleration.

 

However as Mordred pointed out earlier, you could do this for any common density assuming a homogeneous isotropic state existed. The issue is you'd need the values for the Hubble variable which I'm still looking into. But for my purposes, finding even an average deceleration over time would suffice.

 

For calculating acceleration over time, since it's such a symetricle statement, I thought it would be easy to simply rearrange the formulas and solving for dv/dt. Unfortunately, I forgot that an equivalent form of the Hubble constant (inverse of Hubble distance) is needed.

 

I may have to solve both for the lookback timeframe instead which should also verify what I need. In fact it may be preferred since I don't actually believe claim that requires proper time for many reasons including:

 

• No timeframe would ever define proper time no matter what position or velocity the observer was in.
• It can be shown that such a state is nonsensical using the properties of simultaneous time.
• And even if we just assumed the universe was in proper time anyway, no object in the universe would be able to see any other object in the universe much less allow their gravity or energy to have any impact on expansion. Its ironic that such a state would be used to prove dark energy.
• Finally, I can't understand how a major property such as dark energy could be validated by projected data defining a hypothetical state that doesn't exist.

As for why I'm doing this excercise if I don't believe in it:

I don't believe in proper time, but I am trying to verify a potential Lorentz transform that GR may have overlooked some how. If such is the case, then I have an idea of what GR is missing. But if I'm wrong then I'd clearly need to reevaluate that hypothesis.

 

That does not represent acceleration. That is a constant rate of expansion.

Isn't dx/dt velocity and dv/dx (different dx) acceleration over a distance?

[

Edited February 19, 2016 by TakenItSeriously

[Strange]

I don't think that independent galaxies that show a trend for velocities increasing/decreasing with time or distance proves acceleration.

 

Correct. It doesn't.

 

It is a deviation from that which shows that expansion is accelerating.

 

 

It's definitely possible, I'm still struggling to find an article that explains the math in a simplistic way without getting too involved with the details behind all the measurements that include multiple measurements for distance.

 

Any simplistic explanation is probably going to be wrong.

 

 

I don't believe in proper time

 

You don't believe in the time that your watch shows? Extraordinary.

[TakenItSeriously]

Any simplistic explanation is probably going to be wrong.

 

I don't understand, so was the method I described involving Hubble's law and scale factors to solve for v₀ not the correct method?

 

 

You don't believe in the time that your watch shows? Extraordinary.

Well, when light speed creates an insignificant delay, it's effectively fine.

 

However for large distances, it doesn't exist since it allows 0 time for information to travel.

[Strange]

I don't understand, so was the method I described involving Hubble's law and scale factors to solve for v₀ not the correct method?

 

No. Apart from anything else, the proper velocity of these distant galaxies is effectively zero. That is why the increasing speed with distance is not due to acceleration. The accelerating expansion means that the scale factor is changing with time.

 

Well, when light speed creates an insignificant delay, it's effectively fine.

 

Proper time is local by definition. If you are worried about light propagation time, you are probably not dealing with proper time.

 

 

However for large distances, it doesn't exist since it allows 0 time for information to travel.

 

I know of no physics that assumes zero travel time (for significant distances)

[Mordred]

When I get a chance later I'll post the proper distance formula, how Hubbles constant evolves with time.

 

You can check my signature on the Cosmo calc. Which is all done to proper distance. If you look under advanced users the formulas are given though they are slightly modified to use Stretch. Which is the inverse of the scale factor.

[TakenItSeriously]

No. Apart from anything else, the proper velocity of these distant galaxies is effectively zero. That is why the increasing speed with distance is not due to acceleration. The accelerating expansion means that the scale factor is changing with time.

 

 

 

Proper time is local by definition. If you are worried about light propagation time, you are probably not dealing with proper time.

 

 

 

I know of no physics that assumes zero travel time (for significant distances)

When I get a chance later I'll post the proper distance formula, how Hubbles constant evolves with time.

You can check my signature on the Cosmo calc. Which is all done to proper distance. If you look under advanced users the formulas are given though they are slightly modified to use Stretch. Which is the inverse of the scale factor.

Ok, I see where I got at least one thing wrong. Every time I mentioned proper time, I was thinking of the definition for proper distance. I'm pretty sure I got the right definition for Hubble's law though (proper distance =fixed timeframe for the universe) even though I was calling it the wrong thing. This still has me worried since that's the time frame that I have a problem with.

 

Also I'm pretty sure I got lost in click drift hitting too many links and may have got the wrong idea about a few things when reading the wrong page.

 

I'm really embarrassed! Sorry for the confusion, and thanks for your help guys. I've got a lot of re-reading to do.

Edited February 19, 2016 by TakenItSeriously

[TakenItSeriously]

If you measure expansion as per Hubbles parameter km/s/Mpc the rate of expansion is slowing down. Since the CMB it's slowed down considerably.)

I somehow missed or forgot this statement after I let myself get lost in the discussion.

 

This does answer one original question, so thanks very much for that.

 

If however you measure expansion via the radius of the observable universe it's accelerating. This is because of the gained Mpc.

Let's say expansion growth is 100% increase for each Mpc.

measure radius.

1

2

4

8

16.

But the rate per Mpc is still 100%.

(Basically the two terms are due to seperation distance between measurement a and b.)

Also, I see that when using percentage of growth instead of units of growth, that makes it consistent with the an increasing rate of expansion.

 

Just to note that using percentage of growth makes it an exponential growth isn't that correct?

 

So just to make sure I have the correct understanding. To put it another way, Is it fair to say:

 

In lookback time the rate of change for distances between galaxies are increasing.

While the rate of change for their respective velocities are decreasing over time.

Therefore, there must be some yet unknown property which we call dark energy that must explain how distances are increasing or getting stretched faster than their respective velocities should allow?

This is why the look back distances relative to us may increase faster than the speed of light.

 

BTW I chose to use lookback time to make sure the effect at least extrapolates back to the state we are taking measurements from. And that the observable universe also demonstrates this property and it's not just limited to viewing the universe in a state of consistent density (at least in the last 5billion years) So galaxies at the edge of the observable universe could eventually fall the outside of the observable universe which we previously thought couldn't happen.

Edited February 23, 2016 by TakenItSeriously

[Mordred]

not bad you have the concept. A better terminology would be the acceleration is an acceleration of the seperation distance, not the rate of expansion per Mpc.

 

 

I

In lookback time the rate of change for distances between galaxies are increasing.
While the rate of change for their respective velocities are decreasing over time.

Therefore, there must be some yet unknown property which we call dark energy that must explain how distances are increasing or getting stretched faster than their respective velocities should allow?
This is why the look back distances relative to us may increase faster than the speed of light.

BTW I chose to use lookback time to make sure the effect at least extrapolates back to the state we are taking measurements from. And that the observable universe also demonstrates this property and it's not just limited to viewing the universe in a state of consistent density (at least in the last 5billion years) So galaxies at the edge of the observable universe could eventually fall the outside of the observable universe which we previously thought couldn't happen.

 

 

the universe will expand without DE, just to be clear the DE is needed to expalin why the rate between galaxies or Observable universe radius isnt slowing down.

 

we can measure a relative velocity faster than c above the Hubble horizon which is c* age of the universe.

 

Yuo already know recesive velocity is only an apparent but not real velocity.

 

well done. +1

Edited February 23, 2016 by Mordred

[TakenItSeriously]

not bad you have the concept. A better terminology would be the acceleration is an acceleration of the seperation distance, not the rate of expansion per Mpc.

 

 

 

 

 

 

the universe will expand without DE, just to be clear the DE is needed to expalin why the rate between galaxies or Observable universe radius isnt slowing down.

 

we can measure a relative velocity faster than c above the Hubble horizon which is c* age of the universe.

 

Yuo already know recesive velocity is only an apparent but not real velocity.

 

well done. +1

Great, thanks for all the help!