Hubble Law and the combination of acceleration with delay.

[michel123456]

Speculation: Hubble's Law is the natural result of observation from an accelerated point of vue combined with the delay imposed by the constancy of the Speed Of Light.

 

In order to explain the concept, I will take a simple example of the combination of acceleration with delay.

 

You are sitting in your car, waiting at the red light. There is a car in front of you, and another car behind you.

At T=0, the red light turns green, and the first car starts.

After one second, you start.

After 2 seconds, the car behind you starts. The one second gap is the delay.

What are you observing?

The car in front of you accelerates. You are accelerating too, but the gap of one second between the 2 cars provoques an increasing distance. If both cars have the same acceleration, you will observe the preceding car getting away.

What about the car behind you? If you look in the mirror, you will observe that the distance is also increasing, for the exact same reason.

So, in this situation, where all cars have the same acceleration combined with a 1 sec. delay, all observators will see the distance between the cars increase. The distance between the 3 cars is actually increasing, it is an expanding configuration.

 

Now, forget the cars.

 

In the universe, there are no red lights. But there is light.

Light propagates at SOL. Because SOL is a constant, the image we get of the universe is delayed. The further we look, the more the delay.

When we look at a galaxy 100 Light Years away, we are looking at the galaxy as it was 100 years ago. Exactly as if we looked at a car not 1 sec. behind us, but 100 years behind us. The delay is 100 years.

 

So, IF (if) we are accelerating, and IF (if) we are accelerating at the same rate, we should not be surprised to observe this galaxy receding from us. And what is most interesting, is that the further the Galaxy will be, the more receding it will be. The receding speed will observe a simple law increasing proportionaly in function of the distance. Exactly as predicted by Hubble's Law.

 

From a rough calculation, a standard universal acceleration of about 7 10^-10 m/s^2 gives a good approximation of Hubble's Law.

Edited May 23, 2010 by michel123456

[michel123456]

[math]a = Ho\ C[/math]

 

Where

[math]a[/math] universal acceleration (m/s^2) hypothetical.

[math]Ho[/math] Hubble constant (2.29×10−18 s−1)

[math]C[/math] Speed Of Light (299,792,458 m/s)

[Spyman]

"Astronomers have glimpsed what may be the farthest galaxy we've ever seen, providing a picture of a baby galaxy born soon after the beginning of the universe."

http://www.space.com/scienceastronomy/080212-farthest-galaxy.html

 

The galaxy A1689-zD1 has an estimated distance of 12.8 billion lightyears.

 

What is the young galaxy's receding speed from Earth?

[michel123456]

Since we are in Speculations, I dare to say I don't believe it is a young galaxy.

 

It is a galaxy. Far away. As it was a long time ago. Receding, as my cars do, because we see it as it was a long time ago. The adjective "young" is a conclusion inferred by the Big Bang Theory. And I am not a BBer.

[Spyman]

I didn't ask about the age of the galaxy, I wanted to see a calculation from your "car" model how fast it was receding from us when it emitted the light we observe now.

[michel123456]

Using Hubble constant.

V = Ho D (1) (the standard equation)

 

Then with Ho = C/a (2)

 

V= C D / a (3)

 

which gives exactly the same numerical result.

 

Numerically....

I must have been too tired yesterday, I woke up this morning and erased the last part of this post.

Edited May 27, 2010 by michel123456
Consecutive posts merged.

[Spyman]

The equation in post #2 seems to be in conflict with equation (2) in post #6.

[michel123456]

aargh. I was very tired yesterday........

 

No excuse.

 

Again:

 

Using Hubble constant.

V = Ho D (1) (the standard equation)

 

Then with Ho = a/C (2bis)

 

V= a D / C (3bis)

---

Merged post follows:

Consecutive posts merged

If you take a second thought about it, what is that all about?

 

Take a constant (Hubble's constant), multiply with another constant © and you obtain...another constant (a).

 

The question is to realize whether this new constant represents something real, or whether it represents nothing.

 

If it represents nothing, simply throw it away.

If it represents something, what is it?

The new constant, a, is an acceleration.

It corresponds to a phenomena represented in the car example. Formula follows naturally: you just have to input that the delay is caused by C.

Just as we were living in a world in constant acceleration.

Edited May 27, 2010 by michel123456

[Spyman]

Your math is missing a very important piece, your model includes an acceleration so you should realize that the receding speed and distance between the cars would also depend on the duration of previous acceleration and not only on the delay caused by their distance to each other.

 

Without considering the previous acceleration your "car" model fails to explain expansion, because then both the preceding car and the car behind would be at the same distance from the middle car. A car that has been accelerating for 5 seconds looking back at a car 1 second behind will measure a different distance than a car that has been accelerating for 6 seconds looking back at a car 1 second behind.

 

The Hubble constant is not a fixed constant like lightspeed, the Hubble value is constant over distance but it changes over a duration of time. The Hubble constant of 71 km/s/Mpc tells us how fast space is expanding today, how a galaxy placed at a certain distance is receding now, it does not directly tell us how fast something was receding at that distance a very long time ago.

 

According to current models of expansion A1689-zD1 was receding from us with the speed of ~2.90-3.26×c and was ~3.29-3.96 Gly distant when the the light that reaches us now was emitted 12.8 Billion years ago.

 

According to how you use the equations A1689-zD1 was 12.8 Billion lightyears distant and receding from us with the speed of ~0.93×c when the light was emitted, which does not match observations.

Edited May 28, 2010 by Spyman
Clarifying

[michel123456]

Agree.

But because the delay is caused by C, we know that the distance & the delay are linked. The distance measured to an object is also the delay, because C is constant.

When D=1000 LY, T(delay) is 1 Year. Roughly.

 

So, 2 elements of the equation are known. When a is known, only v is unknown.

 

The equations give V (not D) as difference of velocity between 2 objects.

 

-------------------------

[math]v=d/t[/math]

[math]a=v/t[/math]

[math]d=1/2 at^2[/math]

 

Let's suppose 2 objects (p) & (q)

 

[math]D=d_p-d_q[/math] (4) where [math]D[/math] is the distance between the 2 accelerated objects.

 

We know that [math]T=t_p-t_q[/math] (5) where [math]T[/math] is the time interval, the delay.

and we know that

[math]D=c\ T[/math] (6) where [math]c[/math] is Speed Of Light

 

then

 

[math]D=c\ t_p-t_q[/math](7)

and thus

[math]t_p-t_q=D/c[/math](8)

 

The difference of velocity is [math]V=v_p-v_q[/math](9)

and

[math]v_p=at_p[/math](10)

[math]v_q=at_q[/math](11)

V=a(t_p-t_q)(12)

 

replacing [math](t_p-t_q)[/math] with [math]D/c[/math]see(8)

 

we obtain

 

[math]V=a D/c[/math] or

 

[math]V=\frac{a}{c} D[/math] (11)

 

Hubble's Law is [math]V=H_o D[/math] (1)

 

The speculation of this thread is that [math]\frac{a}{c}=H_o[/math] by comparison of (11) & (1) see also(2bis)

Edited May 28, 2010 by michel123456

[Spyman]

Let's suppose 2 objects (p) & (q)

 

[math]D=d_p-d_q[/math] (4) where [math]D[/math] is the distance between the 2 accelerated objects

Which distance is D, the distance between them when the light was emitted, the distance light has to travel between them or the distance they have between them when the light is received?

 

If the two objects are accelerating then the distance will not stay constant during the time interval T.

 

----------

 

IF the speculated acceleration represents something real, it has implications that needs to fit with observations otherwise it is wrong.

 

To put forth this spekulation and make the claim, you also need to explain how this acceleration is able to give rise to measured redshifts from distant galaxies.

[michel123456]

Hm.

 

[math]d_p[/math] is distance at time [math]t_p[/math]

[math]d_q[/math] is distance at time [math]t_q[/math]

 

The difference [math]D=d_p-d_q[/math] is the distance between the 2 objects in the interval [math]T=t_p-t_q[/math].

At each interval [math]T[/math] corresponds a distance [math]D[/math], something that corresponds to observation*.

 

Because I use to discover old discoveries, before jumping into more speculative steps, or confirmation based on observation as you proposed, my first step consists in investigating existing theories. In 99% of the cases, it already exist somewhere.

In this case, i found (almost) nothing, at least from a theoretical point of view.

 

*here you have to remember some older post where i suggested that all observable objects are upon the surface of the past light cone. If you disagree with that, there is no way to proceed further.

[Spyman]

[math]d_p[/math] is distance at time [math]t_p[/math]

[math]d_q[/math] is distance at time [math]t_q[/math]

 

The difference [math]D=d_p-d_q[/math] is the distance between the 2 objects in the interval [math]T=t_p-t_q[/math].

At each interval [math]T[/math] corresponds a distance [math]D[/math], something that corresponds to observation*.

Well, I interpret that as D is the distance light has to travel through space from object q to object p.

 

The distance D you are using in your calculations is thus not the same distance as mentioned in the Hubble Law.

 

As I said back in post #9, the Hubble constant yields the value of how much space is expanding over a certain distance today, as in right now, it does NOT tell you how much space expanded several Billions years ago or how much it has expanded during the last Billions of years.

 

Using the Hubble constant wrongly does not give redshifts corresponding to observations.

[michel123456]

My formula does not change an inch of the results given by Hubble's Law. In fact, Hubble's Law is presumed to be correct in order to give acceleration a. If Hubble's Law predicts the correct redshift, so will a.

 

There are 3 elements:

Ho

C

a

The first 2 elements give the third. If the first ones are correct, then the third one must be correct too, under the condition of being correctly associated of course.

 

------------

Thank you for your replies.

[Spyman]

Hubble's law needs a cosmological model to correctly predict the redshift for distant objects, because the rate of expansion and thus the Hubble constant is changing over large timescales.

 

The Hubble value H₀ tells us how fast a spinning reel on a gigantic fishing rod with the hook stuck on a galaxy far away would spin, while deploying more fishing line because of expansion, in relation to how distant the galaxy is or how much fishing line there are streached between the rod and the hook.

 

However if the distant galaxy would send information towards us, either by a spaceprobe or with a lightray, the information would have to travel through more space than the current distance during the time of transmission, since the distance would increase while the information is on its journey.

 

This longer distance would also cause the "delay" time to be greater and without corrections for this the "acceleration" model will predict wrong receding speed.

 

 

In the OP you said: "So, IF (if) we are accelerating, and IF (if) we are accelerating at the same rate..."

 

But IF the Hubble constant is changing over time, then we are accelerating with a different rate than the object transmitting the image reaching us from over a large time and distance.

 

 

"Hubble's law is considered a fundamental relation between recessional velocity and distance. However, the relation between recessional velocity and redshift depends on the cosmological model adopted, and is not established except for small redshifts.

 

For distances D larger than the radius of the Hubble sphere r_HS , objects recede at a rate faster than the speed of light:

[math]r_{HS}=\frac{C}{H_o}[/math]

Inasmuch as the Hubble "constant" is not constant at all, but varies with time in a manner dictated by the choice of cosmological model, the radius of the Hubble sphere may increase or decrease over various time intervals. The subscript '0' indicates the value of the Hubble constant today."

 

"A variety of possible recessional velocity vs. redshift functions including the simple linear relation v = cz; a variety of possible shapes from theories related to general relativity; and a curve that does not permit speeds faster than light in accordance with special relativity. All curves are linear at low redshifts."

http://en.wikipedia.org/wiki/Hubble's_law

[michel123456]

I have nothing to say against that. it is much probable that the relation [math]a = Ho\ C[/math] is an approximation.

Nevertheless it gives an indication that we are living in an accelerated world.

 

 

In the OP you said: "So, IF (if) we are accelerating, and IF (if) we are accelerating at the same rate..."

 

But IF the Hubble constant is changing over time, then we are accelerating with a different rate than the object transmitting the image reaching us from over a large time and distance.

 

Yes, maybe we are accelerating at a different rate. Which means not acceleration, but accelerated acceleration. I don't want to go into that because I fell like making speculations on speculations.

 

If we keep the simple idea of "living in an accelerated world", what does that mean, in practice & in theory?

 

For example, if this acceleration is a simple consequence of Hubble's Law, it must be related to some kind of cosmological motion. But if we encounter this acceleration in some theoretical construct, such as GR or other, it may not be related to a cosmological model, but to something more fundamental.

[Spyman]

You can lead a horse to water, but you can't make it drink...

[michel123456]

I am patient. The horse will get thirsty.

 

Here is a horse that likes water:

 

Edited June 2, 2010 by michel123456