Constant Acceleration 2

[losfomot]

OK.. let's say I'm in a ship that accelerates away from Earth at an acceleration of 20m/s/s and then maintained that same thrust forever... At some point, wouldn't I have traveled far enough and fast enough, that I would have left Earth's hubble sphere, and therefore be traveling away from Earth at a velocity faster than light?

[swansont]

Doesn't the Hubble sphere expand at c?

 

(GR isn't my area)

[losfomot]

Doesn't the Hubble sphere expand at c?

 

I don't think the 'Hubble Sphere' itself expands at c... I believe that the edge of the hubble sphere is the point where galaxies and such are receding from us at c (due to the expansion of space)... the point where the observable universe ends. However, each point in the universe has it's own, different, hubble sphere. So the more distance and velocity you put between yourself and the Earth, the bigger the difference in your Hubble Spheres. So what I am wondering is if you accelerate for long enough, will you ever put enough velocity and spacial distance between yourself and Earth such that you will leave Earth's Hubble Sphere... effectively traveling away from Earth faster than light?

[swansont]

The radius of the Hubble sphere is the point where objects are receding at c. Why wouldn't it expand at c? That's why, AFAIK, that if the observable universe is 14.7 BLY, we say that it's 14.7 BY old. When the radius was 10 BLY, it was 10 BY old.

[losfomot]

I hate arguing with a physics expert, because I will probably put my foot in my mouth... on that note, I have to disagree with you.

 

The hubble constant is somewhere between 50 and 80 km/s/Mpc... lets use an average of 65km/s/Mpc.

 

1 Mpc = 3,262,000 LY

 

So, for every 3,262,000 LY of distance, an objects velocity of recession increases by 65km/s

 

c = 300,000 km/s

 

300,000 km/s divided by 65 km/s is 4615.384615 (Mpc)

 

4615.384615Mpc x 3,262,000 LY per Mpc = 15.055 Billion LY

 

So at about 15 billion LY objects are receding at the speed of light. This is a set distance... in 5 billion years from now, the point where objects recede at c will still be 15 billion light years away as long as the hubble constant remains constant. In fact, it has (not so) recently been thought that the recession velocity (ie the expansion of space) actually INCREASES over time... that its speeding up. If this is true then our OBSERVABLE universe is actually SHRINKING, not expanding at c.

 

OK.. I'm ready for that foot.

[John Cuthber]

"OK.. let's say I'm in a ship that accelerates away from Earth at an acceleration of 20m/s/s and then maintained that same thrust forever... "

Oops! You cannot assume that because it's not possible. Please read up on relativity.

[losfomot]

"OK.. let's say I'm in a ship that accelerates away from Earth at an acceleration of 20m/s/s and then maintained that same thrust forever... "

Oops! You cannot assume that because it's not possible. Please read up on relativity.

 

Obviously I would need an imaginary never ending fuel source for this to be possible, but as far as relativity is concerned I don't see the problem.

[swansont]

I hate arguing with a physics expert, because I will probably put my foot in my mouth... on that note, I have to disagree with you.

 

The hubble constant is somewhere between 50 and 80 km/s/Mpc... lets use an average of 65km/s/Mpc.

 

1 Mpc = 3,262,000 LY

 

So, for every 3,262,000 LY of distance, an objects velocity of recession increases by 65km/s

 

c = 300,000 km/s

 

300,000 km/s divided by 65 km/s is 4615.384615 (Mpc)

 

4615.384615Mpc x 3,262,000 LY per Mpc = 15.055 Billion LY

 

So at about 15 billion LY objects are receding at the speed of light. This is a set distance... in 5 billion years from now, the point where objects recede at c will still be 15 billion light years away as long as the hubble constant remains constant. In fact, it has (not so) recently been thought that the recession velocity (ie the expansion of space) actually INCREASES over time... that its speeding up. If this is true then our OBSERVABLE universe is actually SHRINKING, not expanding at c.

 

OK.. I'm ready for that foot.

 

 

As I already noted, GR isn't my area. I am by no means an expert at this.

 

However, I note from Davis and Lineweaver's "Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the universe"

http://arxiv.org/abs/astro-ph/0310808

 

"the radius of the Hubble sphere increases with time"

 

They also note that the Hubble constant changes with time; it has a different value during inflation

[someguy]

you can't accelerate at any rate forever because the object being accelerated requires more and more energy to accelerate it the faster it goes because it becomes more massive as the velocity increases and eventually the amount of energy required to accelerate it becomes too great. that's why they say the speed of light is the speed limit.

[swansont]

you can't accelerate at any rate forever because the object being accelerated requires more and more energy to accelerate it the faster it goes because it becomes more massive as the velocity increases and eventually the amount of energy required to accelerate it becomes too great. that's why they say the speed of light is the speed limit.

 

One needs to qualify this (and really, any statement in relativity) with what observer is saying it. An external observer will see different things than the person accelerating. It's relative to your frame. (Gee, imagine that)

 

You won't see me accelerating at a constant rate, even if I maintain it from my reference frame.

[losfomot]

you can't accelerate at any rate forever because the object being accelerated requires more and more energy to accelerate it the faster it goes because it becomes more massive as the velocity increases and eventually the amount of energy required to accelerate it becomes too great. that's why they say the speed of light is the speed limit.

 

 

I, in my ship, would feel a constant acceleration of 20 m/s/s for the entire trip. Earth, watching my ship, would see me initially moving away at 20 m/s/s... but, as I pick up speed, Earth would see my acceleration slowing down to a greater and greater degree. Relative to Earth, I will not accelerate to or beyond the speed of light. (although this is not necessarily true, hence my original post) The point is, I can accelerate at a constant value for as long as I want, there is no 'law of physics' that says I can't and it will not take any 'extra' energy to do so. My acceleration will simply be interpreted differently depending on the observers reference frame.

[losfomot]

However, I note from Davis and Lineweaver's "Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the universe"

http://arxiv.org/abs/astro-ph/0310808

 

Thank you for that link, I'm still trying to wrap my head around the article, there is a lot of information there.

 

They also note that the Hubble constant changes with time; it has a different value during inflation

 

Of course, by definition it must. During inflation the Hubble Constant was higher which made our Hubble Sphere smaller.

 

the Hubble constant during inflation was much larger than subsequent values. Thus the distance to the Hubble sphere was much smaller.

 

"the radius of the Hubble sphere increases with time"

 

In a universe that is currently accelerating, I don't see how this is possible. But if you look at their diagrams depicting 'co-moving' motion, the Hubble Sphere appears to be getting smaller on the 'now' timeline. We can't see it yet because our past light cone hasn't caught up yet, our past light cone touches the Hubble Sphere at a point where the radius of the Hubble Sphere is still increasing with time.

 

The size of our universe and the size of the Hubble Sphere are two very different things. And the only way I could see the Hubble Sphere expanding at c is if the Universe was collapsing... which doesn't appear to be the case.

 

Back to my Question... It does seem clear that as you move away from the Earth, your Hubble Sphere changes from Earth's... You see more of the universe in your direction of travel all the time... and you see less of the universe in the direction you are leaving. So my question (rephrased) is: If you travel at a constant acceleration away from the Earth, will you eventually have a Hubble Sphere in which the Earth is not a part of?

[swansont]

Upon reading further, I see they also say that things are model dependent, and while they say that the sphere is expanding (presumably under some conditions/assumptions/models) that it is not at c.

 

And some of my confusion lies within the misconceptions that are addressed. I see that the particle horizon is indeed beyond the hubble sphere, which would indicate that you are correct that you could get outside of the hubble sphere, under the right conditions. At least, something did in the past.

[Spyman]

Please don't choke on your foot now, losfomot.

 

 

How about this analogy:

 

Lets say you have a rope, (space), which is able to strech infinite. You tie one end to your house, (the Earth), and the other to the rear bumper of your car, (CMB), so the rope is straight and 10 m. Stick a map pin, (a distant star), through the rope in the middle between your house and car.

 

A friend of yours takes off with your car with the speed of 10 m/s and the rope begins to stretch.

 

The point where the rope is streching, (moving away from the house), with 5 m/s is where the map pin is.

So you see, as the rope gets streched the distance to the pin increases.

 

The point where the rope streches with a choosen constant speed is moving away from your house and as long as the car continues with constant speed, the point is disappearing with the same constant speed too.

 

The confusion seems to arise when the car changes speed. Even if your friend would double the speed, the point continues to move away from your house, but during the cars acceleration we need to move the pin backwards to a quarter to keep a constant speed of 5 m/s.

 

The speed of a point which are moving away with constant speed is also dependent of the acceleration of the car. The rate of the acceleration determines how fast we have to move the pin towards the house relative it's position on the rope. (Or towards the car during decceleration.)

 

If the car is able to continue to accelerate with a highly enough rate, then the rate of the acceleration can force the point closer to the house.

 

 

Now to answer your question, it depends on how the Universe will continue to behave...

 

Some of the extreme models predicts a Big Rip where everything will be torn apart to particles which will leave each others horizons due to expansion. So you might spare the effort and just wait here on Earth.

 

In the other extreme end, models predicts a Big Crunch where everything will end up in a universal sized Black Hole. In those cases your spaceship will not be able to leave Earth behind.

 

I think most astrophysical data to date is consistent with a nearly flat universe that will not collapse and continue to accelerate. And if the Universe continues to expand with increasing rate, your spaceship will eventually reach your goal. But you will find yourself very very lonely out there in a dark Universe and not be able to return.

(And very very old too. )

 

Over the next 100 billion years, dark energy is expected to accelerate the most distant galaxies and stars in the universe beyond the speed of light, meaning that they will be invisible to future observers. Some objects once visible at half the universe's current age of about 13.7 billion years are already invisible from the farthest vantage points, and in about 10 trillion years, only the local cluster of galaxies, including our own Milky Way, will be visible, researchers said.

http://www.space.com/scienceastronomy/070501_scietues_futureuniverse.html

[losfomot]

How about this analogy:

 

Lets say you have a rope, (space), which is able to strech infinite. You tie one end to your house, (the Earth), and the other to the rear bumper of your car, (CMB), so the rope is straight and 10 m. Stick a map pin, (a distant star), through the rope in the middle between your house and car.

 

A friend of yours takes off with your car with the speed of 10 m/s and the rope begins to stretch.

 

Thank you for that...

 

Now let's see if I have this right...

 

A Hubble CONSTANT would show the Hubble Sphere to be receding at c.

 

And an accelerating expansion (a hubble not so constant) would cause the Hubble Sphere to continue receding but at a speed less than c... the amount less than c would depend on the value of acceleration.

This would mean that the Sphere is getting larger in terms of distance, but smaller in terms of the amount of spacetime it encompasses.

 

Further, a decelerating universe would have a Hubble Sphere that recedes faster than c.

 

is this right?

[Spyman]

Yes, at least thats how I interpret it, non-expert and all that...

 

The expansion have been decelerating for a long time and that's way we can observe things like the CMB, (z~1100), which was receding with ~57 x c when the light was emitted and is now receding with ~3 x c.

 

This thread deals with the expansion in general and I think it's a good read: http://www.scienceforums.net/forum/showthread.php?t=26714

 

I will cut down and post a quote of Martin, from the thread:

It is actually easy, H is "Hubble parameter" you type in 71 because

the recession speed increases by 71 km/s for every Megaparsec you go out.

It's measured.

 

And Omega_Matter (also called Omega for short) is the "matter fraction" the percentage of the energy density that is matter (either dark or ordinary).

It is 27 percent.

 

And Omega_Lambda (also called Lambda for short which is kind of sloppy notation) is the "dark energy fraction and it is estimated 73 percent.

 

You have to kind of take it on faith for now. They put a lot of effort getting these estimates as good as possible.

 

I will get the URL for Morgan's calculator. It gives the recession SPEEDS.

 

http://www.uni.edu/morgans/ajjar/Cosmology/cosmos.html

 

Playing around with the z number, (redshift of emitted light due to expansion), in Morgans calculator, shows that the farthest we actually can see today, is objects with z=2 which where ~5.7 BLY distant when they emitted the light that reaches us now. Everything else was closer when the light was emitted, (but with lower z closer in time).

 

[EDIT]

Well, not actually the farthest we can see today, it's the farthest point which the light was emitted from.

[losfomot]

Yes, at least thats how I interpret it, non-expert and all that...

 

And it seems to make sense... Of course it means that the Hubble constant should actually be referred to as the Hubble parameter (as Martin refers to it, and as I will from now on) because, it must be getting smaller all the time (despite the fact that the universe seems to be accelerating), and it must have been a pretty huge number for the first little while.

 

The expansion have been decelerating for a long time and that's way we can observe things like the CMB, (z~1100), which was receding with ~57 x c when the light was emitted and is now receding with ~3 x c.

 

This does not seem right. "The expansion have (has) been decelerating"?

[foodchain]

I am confused as to the acceleration, being if its constant does that not sort of state some absolute frame of reference?

[CPL.Luke]

actually the hubble radius is around 50-100 billion ly, do to inflation

[Spyman]

This does not seem right. "The expansion have (has) been decelerating"?

Well, if the Hubble parameter have been "getting smaller all the time", what does that tell you about the rate of expansion? It's only recently the acceleration has started.

http://en.wikipedia.org/wiki/Image:Universes.GIF

 

 

I am confused as to the acceleration, being if its constant does that not sort of state some absolute frame of reference?

The Hubble constant is NOT constant, and the acceleration is not either.

 

 

actually the hubble radius is around 50-100 billion ly, do to inflation

Wrong - The Hubble radius is where the recession velocity = c due to expansion.

(The Hubble radius is neither the particle horizon or the event horizon.)

 

[MATH]{D}_{H}= \frac{c}{H(t)}[/MATH] With H=71 km/s/Mpc -> D= ~13.7 BLY

 

The most distant object we can see now is the CMB with z~1100 which is thought to be ~45 BLY distant from us now, but what we actually see today is a ~14 BY old signal from an old distance of ~0.04 BLY.

 

If the expansion continues to accelerate we are not ever going to see what happened to the particles emitting the CMB, at the distance now ~45 BLY.

[losfomot]

Well, if the Hubble parameter have been "getting smaller all the time", what does that tell you about the rate of expansion?

 

The Hubble parameter would be 'getting smaller all the time' whether the expansion is accelerating or decelerating. As long as the universe is expanding at all, the Hubble parameter would be getting smaller with time.

 

With a constant expansion (no acceleration either way) I believe the Hubble parameter would halve everytime the universe doubled in age (or, going back in time, the Hubble parameter would double everytime you halved the age of the universe)

 

It's only recently the acceleration has started.

http://en.wikipedia.org/wiki/Image:Universes.GIF

 

They say the universal expansion is accelerating because they looked billions of years into the past and the expansion is faster now than it was back then... so I'm not sure what you mean by 'only recently the acceleration has started'

[Spyman]

The Hubble parameter would be 'getting smaller all the time' whether the expansion is accelerating or decelerating. As long as the universe is expanding at all, the Hubble parameter would be getting smaller with time.

You are right, looking back at my analogy with the flexible rope, the Hubble parameter is not the speed of the car, it's the rate of the expansion. An expanding universe should have a decreasing Hubble parameter and the local expansion of space should always be slowing.

 

But the rate of change of the Hubble parameter can tell us the rate of acceleration.

 

As I view the Big Bang, it began with a very rapid inflation, after which expansion continued due to momentum but with a decreasing rate since it got slowed by gravity, and then later dark energy started to dominate and accelerating the expansion again.

 

So as I interpret it, the rate of expansion has been decelerating.

 

They say the universal expansion is accelerating because they looked billions of years into the past and the expansion is faster now than it was back then... so I'm not sure what you mean by 'only recently the acceleration has started'

Hmm, somehow I got the impression the acceleration started recently...

(Maybe because of misleading "now" in images, like the one I linked.)

 

This image has "today" more appropriately: http://www.space.com/php/multimedia/imagedisplay/img_display.php?pic=070501_matter_universe_02.jpg∩=Measurements+of+the+recessional+velocity%2C+distance+and+age+of+stellar+explosions+called+supernovae+provided+the+first+direct+evidence+that+the+rate+at+which+the+universe+is+expanding+is+increasing.+Credit%3A+NASA.

 

Wikipedia says: "Cosmologists estimate that the acceleration began roughly 9 billion years ago."

 

I don't know if using Morgans calculator this way gives correct values but:

(1 Mpc = 3261600 LY, c = 299792.458 km/s, Omega = 0.27 Lambda = 0.73)

 

z=1100.00 -> age= 00.00 BY, Hubble Radius= 00.725 MLY

z=__55.00 -> age= 00.04 BY, Hubble Radius= 63.245 MLY -> Receding speed of Hubble Sphere 1.56c

z=__20.00 -> age= 00.18 BY, Hubble Radius= 00.275 BLY -> Receding speed of Hubble Sphere 1.51c

z=__10.00 -> age= 00.48 BY, Hubble Radius= 00.726 BLY -> Receding speed of Hubble Sphere 1.50c

z=___5.00 -> age= 01.19 BY, Hubble Radius= 01.792 BLY -> Receding speed of Hubble Sphere 1.50c

z=___2.00 -> age= 03.34 BY, Hubble Radius= 04.863 BLY -> Receding speed of Hubble Sphere 1.43c

z=___1.00 -> age= 05.93 BY, Hubble Radius= 08.101 BLY -> Receding speed of Hubble Sphere 1.25c

z=___0.90 -> age= 06.36 BY, Hubble Radius= 08.571 BLY -> Receding speed of Hubble Sphere 1.09c

z=___0.80 -> age= 06.83 BY, Hubble Radius= 09.072 BLY -> Receding speed of Hubble Sphere 1.07c

z=___0.70 -> age= 07.37 BY, Hubble Radius= 09.604 BLY -> Receding speed of Hubble Sphere 1.05c

z=___0.68 -> age= 07.48 BY, Hubble Radius= 09.714 BLY -> Receding speed of Hubble Sphere 1.00c

z=___0.66 -> age= 07.60 BY, Hubble Radius= 09.825 BLY -> Receding speed of Hubble Sphere 0.93c

z=___0.60 -> age= 07.97 BY, Hubble Radius= 10.164 BLY -> Receding speed of Hubble Sphere 0.92c

z=___0.50 -> age= 08.64 BY, Hubble Radius= 10.751 BLY -> Receding speed of Hubble Sphere 0.88c

z=___0.40 -> age= 09.41 BY, Hubble Radius= 11.357 BLY -> Receding speed of Hubble Sphere 0.79c

z=___0.30 -> age= 10.27 BY, Hubble Radius= 11.973 BLY -> Receding speed of Hubble Sphere 0.72c

z=___0.20 -> age= 11.25 BY, Hubble Radius= 12.591 BLY -> Receding speed of Hubble Sphere 0.63c

z=___0.10 -> age= 12.38 BY, Hubble Radius= 13.196 BLY -> Receding speed of Hubble Sphere 0.54c

z=___0.00 -> age= 13.66 BY, Hubble Radius= 13.772 BLY -> Receding speed of Hubble Sphere 0.45c

 

According to Morgans calculator the acceleration begun ~6 Billion Years ago.

 

So, I was wrong, the acceleration did NOT start recently, as I thought.

[losfomot]

According to Morgans calculator the acceleration begun ~6 Billion Years ago.

 

So, I was wrong, the acceleration did NOT start recently, as I thought.

 

I see how you got those numbers, and the picture they paint looks about how it should, but I wonder if it's legitimate?

 

I tried a much simpler method of measuring the acceleration with Morgans Calculator data, and I got negative results... I made a graph showing 'Distance now' against 'Speed now'

 

z=00.074 - Distance=01BLY - Speed=0.07c

z=00.150 - Distance=02BLY - Speed=0.14c

z=00.229 - Distance=03BLY - Speed=0.21c

z=00.312 - Distance=04BLY - Speed=0.29c

z=00.398 - Distance=05BLY - Speed=0.36c

z=00.488 - Distance=06BLY - Speed=0.43c

z=00.583 - Distance=07BLY - Speed=0.50c

z=00.683 - Distance=08BLY - Speed=0.58c

.........

z=568 - Distance=45BLY - Speed=3.26c

 

As you can see, the resulting graph is virtually a straight line graph, not showing acceleration or deceleration over distance.

[Spyman]

I made a graph showing 'Distance now' against 'Speed now'

...

As you can see, the resulting graph is virtually a straight line graph, not showing acceleration or deceleration over distance.

Yes, the expansion is linear over distance, but the acceleration takes place over time.

[Spyman]

Wikipedia says: "Cosmologists estimate that the acceleration began roughly 9 billion years ago."

LOL, I happened to stumble upon this, Wikipedia seems to be a "little" unsecure about the time too.

 

Cosmologists estimate that the acceleration began roughly 9 billion years ago.

http://en.wikipedia.org/wiki/Dark_energy

 

Cosmologists estimate that the acceleration began roughly 5 billion years ago.

http://en.wikipedia.org/wiki/Accelerating_universe