New proof of Hubble's law. Is space really expand?

[icarus2]

Hello!

I apologize for my poor English.

 

New proof of Hubble's law. Is space really expand?

 

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

I. Introduction

~~~~

3. We have never observed the expansion of space.

 

4. Expansion of the universe and expansion of space are not the same concept.

The fact that the universe expands shows that distance between galaxies become further. This can be explained from the expansion of space between galaxies, but this can be explained even when galaxies have +r direction initial speed in condition where space doesn't expand.

 

 

II. Proof of Hubble's law through dynamics

1. After accelerating expansion(such as inflation) of early universe has almost finished, particles started to have some velocity.

 

This velocity distribution naturally has higher velocity when it is further away from the center of the universe and has lower velocity when it is closer to the center.

 

A. Big bang simulation in the zero energy universe

 

[Video for Big bang Simulation]

Fig.1.Velocity distribution of galaxies at early universe.

Red arrows show the velocity vector of particles. It can be known that the magnitude of velocity vector is bigger as it become further from the center.

 

Even if the velocity of particles is zero in the early universe, there are particles with higher velocity in further areas from the center and particles close to the center have relatively low velocity by inflation. When positive mass gravitationally contracts to form a galaxy, momentum must be conserved, so higher initial velocity continues to exist as it becomes further away from the center of universe.

 

B. Natural distribution of velocity in the 3D space

Thinking in another way, 3 dimensional space can be divided into 3 areas (from the center) to far, middle, and close area. Even if the velocity of the far area is lower than the middle area, middle area particles exceed far area particles when time passes because the velocity of middle particles are higher. As a result, velocity distribution of particles shows that the velocity of far areas is highest, middle area is second, and the close area becomes third.

 

C. Velocity distribution when some kind of anti-gravitational source exists

If some kind of anti-gravitational source in 3 dimension exists, M exists with even density, the above velocity distribution can exist.

 

[math]m\vec a = + \frac{{G(\frac{{4\pi }}{3}r^3 \rho )m}}{{r^2 }}\hat r[/math]

[math]\vec a = + \frac{{4\pi G}}{3}\rho r\hat r[/math]

 

If anti-gravitational source is evenly distributed in accelerating expansion time like the inflation of early universe, a bigger acceleration a exists as r becomes larger and velocity distribution has a higher velocity as the radius of the universe becomes larger. As a result, higher velocity exists for particles of far area from the center of the universe after inflation ends.

 

The 3 explanations shown above mean that higher velocity for larger R(distance from the center of universe) after inflation in the early universe isn't a peculiar phenomenon. If speed in small area in the early universe distributes from 0 to c and if some time passes, velocity distribution will be in order as above.

 

2. Derivation of Hubble's law in space without expansion

A. Decelerating expansion time

First to look into the possibility of this model, let's look into the case in which the direction of V_a1 and V_b1 is the same.

 

V_a1 = V_a0 + ( - a₁t₁ )

V_b1 = V_b0 + ( - a₁t₁ )

 

V_a0, V_b0: It is the speed in which A and B galaxy has when inflation ends.

- a₁: It is the acceleration of decelerating expansion because decelerating expansion seems to have taken place in the early universe. It is actually a function of time. To make the problem simple, we plan to solve the problem making it as a constant.

 

t₁ : Total time of universe decelerating expansion.

[math]R_{a1} = R_{a0} + V_{a0} t_1 - \frac{1}{2}a_1 t_1 ^2[/math]

[math]R_{b1} = R_{b0} + V_{b0} t_1 - \frac{1}{2}a_1 t_1 ^2 [/math]

 

The above equations are equations of speed and distance when acceleration is constant.

 

B. Accelerating expansion time

After decelerating expansion ends, there was a time of accelerating expansion. Acceleration is given as a₂ this time and the duration time is set as t₂.

 

[math]V_{an} = V_{a1} + a_2 t_2 = (V_{a0} - a_1 t_1 ) + a_2 t_2 [/math]

[math]V_{bn} = V_{b1} + a_2 t_2 = (V_{b0} - a_1 t_1 ) + a_2 t_2 [/math]

[V_an,V_bn is the now speed of galaxy a and galaxy b.

 

[math]R_{an} = R_{a1} + V_{a1} t_2 + \frac{1}{2}a_2 t_2 ^2 = R_{a0} + (V_{a0} t_1 - \frac{1}{2}a_1 t_1 ^2 ) + (V_{a0} - a_1 t_1 )t_2 + \frac{1}{2}a_2 t_2 ^2[/math]

[math] = R_{a0} + V_{a0} (t_1 + t_2 ) - a_1 t_1 t_2 - \frac{1}{2}a_1 t_1 ^2 + \frac{1}{2}a_2 t_2 ^2[/math]

 

[math]R_{bn} = R_{b0} + V_{b1} t_2 + \frac{1}{2}a_2 t_2 ^2 = R_{b0} + (V_{b0} t_1 - \frac{1}{2}a_1 t_1 ^2 ) + (V_{b0} - a_1 t_1 )t_2 + \frac{1}{2}a_2 t_2 ^2[/math]

[math] = R_{b0} + V_{b0} (t_1 + t_2 ) - a_1 t_1 t_2 - \frac{1}{2}a_1 t_1 ^2 + \frac{1}{2}a_2 t_2 ^2[/math]

 

C. Deriving Hubble's law (when direction is the same)

[math]V_{rel} = V_{bn} - V_{an}[/math] is the relative speed of galaxy a and galaxy b.

[math]V_{rel} = V_{bn} - V_{an} = (V_{b0} - a_1 t_1 ) + a_2 t_2 - (V_{a0} - a_1 t_1 ) - a_2 t_2 = V_{b0} - V_{a0}[/math]

 

[math]R_{rel} = R_{bn} - R_{an} = R_{b0} + V_{b0} (t_1 + t_2 ) - a_1 t_1 t_2 - \frac{1}{2}a_1 t_1 ^2 + \frac{1}{2}a_2 t_2 ^2 - [R_{a0} + V_{a0} (t_1 + t_2 ) - a_1 t_1 t_2 - \frac{1}{2}a_1 t_1 ^2 + \frac{1}{2}a_2 t_2 ^2 ][/math]

[math]R_{rel} = (R_{b0} - R_{a0} ) + (V_{b0} - V_{a0} )(t_1 + t_2 ) \cong (V_{b0} - V_{a0} )t[/math]

 

Because the galaxies or particles in the early universe were concentrated in a very close distance,

 

it can be set as [math](R_{b0} - R_{a0} ) = 0[/math]

[math]t = t_1 + t_2[/math]

This is the age of the universe.

 

Deriving the relation between V_rel and R_rel,

[math]V_{rel} = V_{bn} - V_{an} = V_{b0} - V_{a0} = \frac{1}{t}R_{rel} = HR_{rel}[/math]

 

It can be known that Hubble's law comes out.

 

Especially, the Hubble constant is H=1/t and this is a result that the Hubble constant in Hubble's law corresponds to the reciprocal of the age of universe. Considering decelerating expansion and accelerating expansion and movement of relative particles, the actual age of the universe is 0.993t_H. It is very close to 1.

 

Therefore, the above model contains simple equation, but has possibility.

 

Thus, the recession velocity and Hubble's law between galaxies don't come from some vague concept (unknown concept without empirical experience) of "expansion of space" and shows possibility that it comes from a simple movement equation called [math]R = V_0 t + \int {\int {a(t)d^2t} }[/math]

 

In [math]R = V_0 t + \int {\int {a(t)d^2t} }[/math], if a(t)(acceleration) is small, this is because a [math]V_{rel} = \frac{1}{t}R_{rel} = HR_{rel}[/math] shape Hubble's law comes out.

 

D. The observation of "all galaxies become further from us and all galaxies have recession velocity from Hubble's law" isn't from the expansion of space, it is result of dynamics that galaxies show.

 

Fig.2.Hubble's observation of all galaxies receding with Earth in the center

 

It is assumed that interpretation issues of observation results above applied most in physicists and astronomers introducing expansion of space. When observed from Earth, it is observed that all galaxies recede from Earth and the recession velocity also follow all relations of [math]\vec V = H\vec R[/math].

To explain this, if position of the Earth is the center of expansion, namely if position of the Earth is the center of universe, this issue can be simply solved but it can be clearly known that Earth isn't the center of the universe from the observation of the universe until now.

 

It is because Earth isn't the center of the solar system, but is clear to be just a planet and that the solar system isn't the center of the galactic system either.

 

Therefore, physicists and astronomers had to find a way to explain this and as this couldn't be explained by dynamics, a new concept that "space expands" was introduced. To explain more specifically, it is assumed that the stereotype that Hubble's observation isn't valid in places where isn't the center of expansion had influence.

 

 

[ Derivation of Hubble's law ]

 

Fig.3. Hubble's law doesn't result from the expansion of space, but is a dynamical result from the movement of galaxies in space.

 

Set as [math]|\vec a_{E1} | = |\vec a_{\alpha 1} | = |\vec a_{\beta 1} | = |\vec a_{r1} | = |\vec a_{\delta 1} | = a_1[/math][math]|\vec a_{E2} | = |\vec a_{\alpha 2} | = |\vec a_{\beta 2} | = |\vec a_{\gamma 2} | = |\vec a_{\delta 2} | = a_2[/math]

[math]\vec V_{E1} = \vec V_{E0} - \vec a_{E1} t_1[/math]

[math]\vec V_{\alpha 1} = \vec V_{\alpha 0} - \vec a_{\alpha 1} t_1[/math]

[math]\vec V_{En} = \vec V_{E1} + \vec a_{E2} t_2 = (\vec V_{E0} - \vec a_{E1} t_1 ) + \vec a_{E2} t_2 = ((V_{E0} - a_1 t_1 ) + a_2 t_2 )\hat x[/math]

Set as x-axis.

 

[math]\vec V_{\alpha n} = \vec V_{\alpha 1} + \vec a_{\alpha 2} t_2 = (\vec V_{\alpha 0} - \vec a_{\alpha 1} t_1 ) + \vec a_{\alpha 2} t_2[/math]

[math]= (V_{\alpha 0} - a_{\alpha 1} t_1 + a_{\alpha 2} t_2 )\cos \theta \hat x + (V_{\alpha 0} - a_{\alpha 1} t_1 + a_{\alpha 2} t_2 )\sin \theta \hat y [/math]

[math]= (V_{\alpha 0} - a_1 t_1 + a_2 t_2 )\cos \theta \hat x + (V_{\alpha 0} - a_1 t_1 + a_2 t_2 )\sin \theta \hat y [/math]

 

[math]\vec R_{En} = \vec R_{E1} + \vec V_{E1} t_2 + \frac{1}{2}\vec a_{E2} t_2 ^2 = (\vec V_{E0} t_1 - \frac{1}{2}\vec a_{E1} t_1 ^2 ) + (\vec V_{E0} - \vec a_{E1} t_1 )t_2 + \frac{1}{2}\vec a_{E2} t_2 ^2[/math]

[math]= (t_1 + t_2 )\vec V_{E0} - t_1 t_2 \vec a_{E1} - \frac{1}{2}t_1 ^2 \vec a_{E1} + \frac{1}{2}t_2 ^2 \vec a_{E2}[/math]

 

[math]\vec R_{En} = [(t_1 + t_2 )V_{E0} - t_1 t_2 a_1 - \frac{1}{2}t_1 ^2 a_1 + \frac{1}{2}t_2 ^2 a_2 ]\hat x[/math]

[math] \vec R_{\alpha n} = \vec R_{\alpha 1} + \vec V_{\alpha 1} t_2 + \frac{1}{2}\vec a_{\alpha 2} t_2 ^2 = (\vec V_{\alpha 0} t_1 - \frac{1}{2}\vec a_{\alpha 1} t_1 ^2 ) + (\vec V_{\alpha 0} - \vec a_{\alpha 1} t_1 )t_2 + \frac{1}{2}\vec a_{\alpha 2} t_2 ^2[/math]

[math] = (t_1 + t_2 )\vec V_{\alpha 0} - t_1 t_2 \vec a_{\alpha 1} - \frac{1}{2}t_1 ^2 \vec a_{\alpha 1} + \frac{1}{2}t_2 ^2 \vec a_{\alpha 2} [/math]

 

[math] \vec R_{\alpha n} = [(t_1 + t_2 )V_{\alpha 0} - t_1 t_2 a_1 - \frac{1}{2}t_1 ^2 a_1 + \frac{1}{2}t_2 ^2 a_2 ]\cos \theta \hat x + [(t_1 + t_2 )V_{\alpha 0} - t_1 t_2 a_1 - \frac{1}{2}t_1 ^2 a_1 + \frac{1}{2}t_2 ^2 a_2 ]\sin \theta \hat y[/math]

 

[ Relative Velocity ]

[math]\vec V_{rel} = \vec V_{\alpha n} - \vec V_{En} = [(V_{\alpha 0} \cos \theta - V_{E0} ) + ( - a_1 t_1 + a_2 t_2 )(\cos \theta - 1)]\hat x + (V_{\alpha 0} - a_1 t_1 + a_2 t_2 )\sin \theta \hat y[/math]

 

[ Relative Distance ]

[math]\vec R_{rel} = t\{ [(V_{\alpha 0} \cos \theta - V_{E0} ) + \frac{1}{t}( - t_1 t_2 a_1 - \frac{1}{2}t_1 ^2 a_1 + \frac{1}{2}t_2 ^2 a_2 )(\cos \theta - 1)]\hat x[/math]

[math]+ [V_{\alpha 0} + \frac{1}{t}( - t_1 t_2 a_1 - \frac{1}{2}t_1 ^2 a_1 + \frac{1}{2}t_2 ^2 a_2 )]\sin \theta \hat y\}[/math]

 

 

1) When Θ is zero.

[math]\vec V_{rel} = (V_{\alpha 0} - V_{E0} )\hat x[/math]

[math]\vec R_{rel} = t(V_{\alpha 0} - V_{E0} )\hat x[/math]

[math]\vec V_{rel} = \frac{1}{t}\vec R_{rel} = H\vec R_{rel} [/math]

Therefore, Hubble's law is valid.

 

 

2) When Θ is small.

[math]\vec V_{rel} \simeq (V_{\alpha 0} - V_{E0} )\hat x + (V_{\alpha 0} - a_1 t_1 + a_2 t_2 )\theta \hat y[/math]

[math]\vec R_{rel} \simeq t\{ [(V_{\alpha 0} - V_{E0} )\hat x + [V_{\alpha 0} + \frac{1}{t}( - t_1 t_2 a_1 - \frac{1}{2}t_1 ^2 a_1 + \frac{1}{2}t_2 ^2 a_2 )]\theta \hat y\}[/math]

 

Hubble's law is valid for the 2 following cases.

 

i) V_E0,V_α0 >> -a₁t₁ + a₂t₂ :When initial speed is much larger than speed change by deceleration and acceleration :

 

* Because there is high possibility that there was a time of inflation of the early universe, particles gained high speed after inflation and the galaxy composed by these particles also had high speed, so the above supposition has validity.

 

* -a₁t₁ + a₂t₂ ~ 0 : When the effects of deceleration and acceleration are offset by each other

==========

Considering decelerating expansion and accelerating expansion and movement of relative particles, the actual age of the universe is 0.993t_H. It is very close to 1. Namely, our universe has a state of -a₁t₁ + a₂t₂ ~ 0

==========

**Ref : Bradley W. Carroll, Dale A. Ostlie. Introduction to Modern Astrophysics. **

 

* Zero Energy Universe : In principle, the total energy is zero. So deceleration and acceleration terms are small.

 

[math]\vec V_{rel} \simeq (V_{\alpha 0} - V_{E0} )\hat x + V_{\alpha 0} \theta \hat y[/math]

[math]\vec R_{rel} \simeq t[(V_{\alpha 0} - V_{E0} )\hat x + V_{\alpha 0} \theta \hat y][/math]

[math]\vec V_{rel} = \frac{1}{t}\vec R_{rel} = H\vec R_{rel}[/math]

Therefore, Hubble's law is valid.

 

ii) Hubble's law is valid in t₁ = t₂ ,a₁ = 3a₂ condition.

 

Because the term of decelerating expansion and accelerating expansion is almost similar from the current observation, it can be set as t₁ = t₂.

 

[math]\vec V_{rel} \simeq[(V_{\alpha 0} (1 - \frac{{\theta ^2 }}{2}) - V_{E0} ) + a_2 t_2 \theta ^2 ]\hat x + (V_{\alpha 0} - 2a_2 t_2 )\theta \hat y[/math]

[math]\vec R_{rel} \simeq t\{ [(V_{\alpha 0} (1 - \frac{{\theta ^2 }}{2}) - V_{E0} ) + a_2 t_2 \theta ^2 ]\hat x + (V_{\alpha 0} - 2a_2 t_2 )\theta \hat y\}[/math]

[math]\vec V_{rel} = \frac{1}{t}\vec R_{rel} = H\vec R_{rel}[/math]

Therefore, Hubble's law is valid.

 

 

3) When Θ is big.

[math]\vec V_{rel} = [(V_{\alpha 0} \cos \theta - V_{E0} ) + ( - a_1 t_1 + a_2 t_2 )(\cos \theta - 1)]\hat x + (V_{\alpha 0} - a_1 t_1 + a_2 t_2 )\sin \theta \hat y[/math]

[math]\vec R_{rel} = t\{ [(V_{\alpha 0} \cos \theta - V_{E0} ) + \frac{1}{t}( - t_1 t_2 a_1 - \frac{1}{2}t_1 ^2 a_1 + \frac{1}{2}t_2 ^2 a_2 )(\cos \theta - 1)]\hat x + [V_{\alpha 0} + \frac{1}{t}( - t_1 t_2 a_1 - \frac{1}{2}t_1 ^2 a_1 + \frac{1}{2}t_2 ^2 a_2 )]\sin \theta \hat y\}[/math]

 

i) V_E0,V_α0 >> -a₁t₁ + a₂t₂

[math]\vec V_{rel} \simeq (V_{\alpha 0} \cos \theta - V_{E0} )\hat x + V_{\alpha 0} \sin \theta \hat y[/math]

[math]\vec R_{rel} \simeq t[(V_{\alpha 0} \cos \theta - V_{E0} )\hat x + V_{\alpha 0} \sin \theta \hat y][/math]

[math]\vec V_{rel} = \frac{1}{t}\vec R_{rel} = H\vec R_{rel}[/math]

Therefore, Hubble's law is valid.

 

When initial speed is much larger than velocity change from deceleration and acceleration, Hubble's law is valid is a very wide area. Also this initial speed is the velocity gained from the inflation process.

 

ii) If t₁ = t₂ ,a₁ = 3a₂

[math]\vec V_{rel} = [(V_{\alpha 0} \cos \theta - V_{E0} ) - 2a_2 t_2 (\cos \theta - 1)]\hat x + (V_{\alpha 0} - a_2 t_2 )\sin \theta \hat y[/math]

[math]\vec R_{rel}= t\{ [(V_{\alpha 0} \cos \theta - V_{E0} ) - 2a_2 t_2 (\cos \theta - 1)]\hat x + (V_{\alpha 0} - 2a_2 t_2 )\sin \theta \hat y\}[/math]

[math]\vec V_{rel} = \frac{1}{t}\vec R_{rel} = H\vec R_{rel}[/math]

Therefore, Hubble's law is valid.

 

E. Direct meaning of proof

1) Hubble's law is valid is a very wide area in 3 dimensional space when the initial speed of galaxies is much larger than the velocity change by deceleration and acceleration (in the same meaning, when velocity change by deceleration and acceleration is smaller compared to initial speed).

 

2) Even though initial velocity isn't much bigger than the effect by deceleration and acceleration, Hubble's law can be valid in some specific condition.

For example, t₁ = t₂ ,a₁ = 3a₂

 

3) Even though Earth isn't the center of the universe, the belief(something not experienced such as "expansion of space”) isn't necessarily needed to explain the reason all galaxies recede from Earth.

 

 

III. Meaning including proof

Hubble's law isn't a matter only explained by special condition such as "center of the universe" or a new concept that we haven't experienced such as "expansion of space."

 

Hubble's law is a result of dynamics valid in almost all areas when change of acceleration is small in the universe.

 

1. Even if -a₁(t) and + a₂(t) is a function of time, Hubble's law is always valid when the effect of decelerating expansion and accelerating expansion is smaller than initial velocity.

 

To derive the Hubble's law, we presumed decelerating expansion in the early term and accelerating expansion of the later term. -a₁ and +a₂ was set as a constant in this process. However, more closely speaking, -a₁ and +a₂ is a function of time.

 

Fig.4. Hubble's law is a dynamical result from the movement of galaxies in 3D space. Two situations are same.

 

4. Therefore, red shift comes from the Doppler shift of light and implies that the existing equation of red shift should be revised.

Existing equation : [math]z = \frac{{R_{obs} }}{{R_{emitted} }} - 1[/math]

R is scale factor.

Doppler shift :[math] z = \sqrt {\frac{{1 + \frac{V}{c}}}{{1 - \frac{V}{c}}}} - 1[/math]

The two equations show similar results in close galaxies(z<2), but show difference in far galaxies.

 

In condition of z<2, difference of distance <5%. By the way, distance in z=2 is over 11Gly.

** Maybe, this result derived from the model [math]\Lambda=0[/math] **

**Ref : Bradley W. Carroll, Dale A. Ostlie. Introduction to Modern Astrophysics. **

 

When we did not have verifiable ability about two models, we decided the final model. Because of the fixed idea that Hubble's observation isn't valid in places where isn't the center of expansion. Therefore, should be given the opportunity of review to non-expandsion model of space(or the movement of galaxies through space).

 

 

On Inflation - expansion faster than light

To explain the flatness and horizon problem, expansion faster than light (inflation) was assumed. However, positive energy and negative energy are cancelled in the zero energy universe. So zero energy universe is flat. Therefore to explain flatness, there is no need to assume expansion faster than light.

 

The horizon problem occurs from the wrong Hubble radius which is derived from the assumption that space expands. If particles don't have velocity faster than light, all areas in the early universe will be inside the area of light(radiation) and are all causally connected. Therefore, thermal equilibrium takes place.

 

We don’t know(or observe) velocity of distant galaxy. We observed only redshift and then, we estimate the scale factor, velocity, distance….

 

Key point of problem, [math]R = \frac{1}{{z + 1}}[/math], it is derived from assumption that space is expanding. (R is scale factor)

 

If space does not expand, R=1/(1+z) is wrong. Therefore, existing velocity and distance derived from redshift eq. are also wrong.

 

In my opinion,

Horizon problem doesn't occur and expansion faster than light isn't needed.

 

 

Space doesn't expand. New proof of Hubble's law and Center of the universe

http://vixra.org/abs/1203.0044

Edited September 20, 2012 by icarus2

[imatfaal]

!

Moderator Note

Whilst interesting this is Speculative in that it challenges accepted physics - moved to Speculations. Please take a moment to read the specific rules of that forum.

[Iggy]

When observed from Earth, it is observed that all galaxies recede from Earth and the recession velocity also follow all relations of [math]\vec V = H\vec R[/math].

To explain this, if position of the Earth is the center of expansion, namely if position of the Earth is the center of universe, this issue can be simply solved but it can be clearly known that Earth isn't the center of the universe from the observation of the universe until now.

 

It is because Earth isn't the center of the solar system, but is clear to be just a planet and that the solar system isn't the center of the galactic system either.

 

Therefore, physicists and astronomers had to find a way to explain this and as this couldn't be explained by dynamics, a new concept that "space expands" was introduced. To explain more specifically, it is assumed that the stereotype that Hubble's observation isn't valid in places where isn't the center of expansion had influence.

 

 

[ Derivation of Hubble's law ]

 

No, I think it is pretty well known that expansion would appear isotropic even if we weren't at the center and without the metric expansion of space. Unfortunately, the best link I could find is talking about white holes, but it gets the idea across,

 

Stellar collapse has been intensively studied since the seminal work of Snyder and Oppenheimer in 1939 and this simple case is well understood. It is possible to construct an exact model of stellar collapse in the absence of pressure by gluing together any FRW solution inside the spherical star and a Schwarzschild solution outside. Spacetime within the star remains homogeneous and isotropic during the collapse.

 

It follows that the time reversal of this model for a collapsing sphere of dust is indistinguishable from the FRW models if the dust sphere is larger than the observable universe.

 

math.ucr.edu

A collapsing sphere of dust isn't something that requires the expansion of space and it would appear isotropic to one of the dust particles that had a limited field of view (couldn't see the edge), so I don't think you can say that "physicists and astronomers had to find a way to explain this and as this couldn't be explained by dynamics, a new concept that "space expands" was introduced."

 

I couldn't really comment on the rest of your conclusions, I'm sorry, I mostly just skimmed your post.

[michel123456]

No, I think it is pretty well known that expansion would appear isotropic even if we weren't at the center and without the metric expansion of space. (...)

 

If I am correct the objects moving tangentially (in the left sketch) should be observed as not receding at all (on the right sketch they should have only lateral speed). That would suggest a specific region* of the sky should be observed as not receding, and as much as I know that is not the case. So I agree with the "no" of Iggy.

 

*i guess a paraboloid of revolution or roughly a disk if the centre is very far away.

[pantheory]

Icarus 2

 

Hubble's law doesn't result from the expansion of space, but is a dynamical result from the movement of galaxies in space.

 

We have never observed the expansion of space.

 

We don't know(or observe) velocity of distant galaxy. We observed only redshift and then , we estimate the scale factor, velocity, distance….

 

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

 

Therefore, Hubble's law is valid.

 

Therefore, red shift comes from the Doppler shift of light and implies that the existing equation of red shift should be revised.

 

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

Icarus 2

 

What is your position on all of this? Do you ascribe to the expansion of the universe? Galaxies expanding away from each other? Space expanding? etc. Do you ascribe to the Hubble formula or only in certain domains?

 

//

Edited September 22, 2012 by pantheory

[Iggy]

If I am correct the objects moving tangentially (in the left sketch) should be observed as not receding at all (on the right sketch they should have only lateral speed). That would suggest a specific region* of the sky should be observed as not receding, and as much as I know that is not the case.

I don't exactly follow. If you shoot a cannonball north and another cannonball northeast the distance between the cannonballs increases over time. Anyone who remains directly between the cannonballs will indeed say that they are both receding.

 

I found a better reference for what I was pointing toward by the way,

 

Turn your attention now to the interior of the ball of dust. The simplest of interiors is that which is homogeneous and isotropic everywhere except at the surface. We will then be looking at an interior locally identical to a dust-filled Friedmann cosmological model... Homogeneity and isotropy are broken at the star’s surface

 

Collapse of a Ball of Dust

[michel123456]

I don't exactly follow. If you shoot a cannonball north and another cannonball northeast the distance between the cannonballs increases over time. Anyone who remains directly between the cannonballs will indeed say that they are both receding.

(...)

 

 

You see that there are 2 sketches in the above image, with an equal sign in-between.

[Iggy]

You see that there are 2 sketches in the above image, with an equal sign in-between.

I'm not amused. Of course that's what it shows.

 

edit:

 

My apologies if you weren't trying to mess with me with that.

 

Yes, the left image shows everything receding from the blue dot. The velocity at which it recedes is proportional to its distance from the blue dot. We are meant to consider how this appears to the black dot -- in particular, would things appear isotropic to the black dot if its observations are limited to the red circle.

 

The answer is yes and it is shown on the right. If the black dot considers itself at rest then the four stars will be moving directly away from the dot at equal speeds.

 

In other words, if you subtract the vector of the black dot on the left from each vector you get the vectors on the right.

Edited September 22, 2012 by Iggy

[icarus2]

Icarus 2

 

What is your position on all of this? Do you ascribe to the expansion of the universe? Galaxies expanding away from each other? Space expanding? etc. Do you ascribe to the Hubble formula or only in certain domains?

//

Dear pantheory,

 

I’m very sorry. I apologize for my poor English.

 

My assertion is that

1. Space does not expand. (I agree that Universe is expanding.)

 

2. Hubble's law is a dynamical result from the movement of galaxies in space.

 

3. [math]R = \frac{1}{z}[/math] is derived from assumption that space is expanding. R=1/(1+z) is wrong because of that space does not expand. But, two equations show similar results in close galaxies(z<2).

...

 

--Icarus2

Edited September 22, 2012 by icarus2

[pantheory]

Dear pantheory,

 

I'm very sorry. I apologize for my poor English.

 

My assertion is that

1. Space does not expand. (I agree that Universe is expanding.)

 

2. Hubble's law is a dynamical result from the movement of galaxies in space.

 

3. [math]R = \frac{1}{z}[/math] is derived from assumption that space is expanding. R=1/(1+z) is wrong because of that space does not expand.

...

 

--Icarus2

 

I've read your material before and think you do quite well in English.

 

I also think that space is not expanding like you have proposed, but go farther in believing that the universe is not expanding either. Some evidence to support this belief is that the local galaxy group and maybe local super-cluster Virgo, does not appear to be expanding. It is thought that gravity compensates for the expansion of space in the local group. There is no evidence that I can think of that the universe is expanding other than the observed redshift of galactic spectra. Although there are seemingly other possible explanations for these redshifts rather than expanding galaxies and space, none of these other possible explanations would be consistent with the Big Bang model. Hoyle's SS models also proposed an expanding but SS universe, so few other explanations of galactic redshifts have much of a following today.

Edited September 22, 2012 by pantheory

[StringJunky]

Dear pantheory,

 

I’m very sorry. I apologize for my poor English.

 

My assertion is that

1. Space does not expand. (I agree that Universe is expanding.)

 

 

How can the universe expand if space is not expanding and preserve isotropy and homogeneity (or don't you think so?)? Your apparent alternative implication is an expanding 'island universe' in a sea of pre-existing space. Also, if redshifting galaxies are accepted, they can't physically move at superluminal speeds (Re: SR), so, space expansion is the only other option or do you assert physical objects can move FTL into a pre-existing space?

[pantheory]

How can the universe expand if space is not expanding and preserve isotropy and homogeneity (or don't you think so?)? Your apparent alternative implication is an expanding 'island universe' in a sea of pre-existing space. Also, if redshifting galaxies are accepted, they can't physically move at superluminal speeds (Re: SR), so, space expansion is the only other option or do you assert physical objects can move FTL into a pre-existing space?

String Junky,

 

There is a fine line between agreeing with a proposal and proposing your own. In the context of the speculation, is space really expanding, I can simply state my opinion, which is simply no. In my case it's more that an opinion but an entire theory. I

 

Also, if redshifting galaxies are accepted, they can't physically move at superluminal speeds (Re: SR), so, space expansion is the only other option or do you assert physical objects can move FTL into a pre-existing space?

My own model is a diminution of matter model. whereby the the expansion of the universe is just a optical allusion. In my studies and mathematical evaluations it would take the reduction of about 1 millionth part every 6,000 years to observe what we are presently observing.

//

//

Edited September 23, 2012 by pantheory

[lazyworks]

the link to my video is not exactly a reply, but a different way to look at expansion. Hope it contributes something..

[imatfaal]

!

Moderator Note

Lazyworks (and to a lesser extent Pantheory) please keep this thread on the OP topic rather that branching off to explain your own theories

[michel123456]

I'm not amused. Of course that's what it shows.

 

edit:

 

My apologies if you weren't trying to mess with me with that.

 

Yes, the left image shows everything receding from the blue dot. The velocity at which it recedes is proportional to its distance from the blue dot. We are meant to consider how this appears to the black dot -- in particular, would things appear isotropic to the black dot if its observations are limited to the red circle.

 

The answer is yes and it is shown on the right. If the black dot considers itself at rest then the four stars will be moving directly away from the dot at equal speeds.

 

In other words, if you subtract the vector of the black dot on the left from each vector you get the vectors on the right.

 

 

I added 2 tangents with intersection points A & B. The vector is tangent to the circle, so if I am correct the observer upon Earth should not observe any receding speed for objects at points A & B.

Note: I understand that the vector at A & B is not parallel to vector at Earth, but in order to observe the vector substraction, you have to wait for several million years. If your measure is instantaneous (IOW seconds, minutes or even years), you cannot measure it. Right? or wrong?

[Iggy]

 

I added 2 tangents with intersection points A & B. The vector is tangent to the circle, so if I am correct the observer upon Earth should not observe any receding speed for objects at points A & B.

Note: I understand that the vector at A & B is not parallel to vector at Earth, but in order to observe the vector substraction, you have to wait for several million years. If your measure is instantaneous (IOW seconds, minutes or even years), you cannot measure it. Right? or wrong?

well, I think the vector would be the same size as all the others on the red circle. Maybe this would be a good way of looking at it,

 

 

So that all of the red lines are the same size, the ones where the tangent is the line of expansion too. It's important also that the lengths are proportional, so for example AB/AD is equal to AC/AE and AF/AG since velocity from the center needs to be proportional to distance.

 

I'm pretty sure the standard wisdom is that this checks out.

 

[edited for having proportional lengths transposed]

Edited September 23, 2012 by Iggy

[icarus2]

Dear, Iggy!

 

WoW!, it is very intuitive.

[lazyworks]

Dear Moderator, thanks for your correction. Can you suggest where I should take my ideas for discussion?

[ACG52]

Dear Moderator, thanks for your correction. Can you suggest where I should take my ideas for discussion?

 

 

Start your own thread in speculations.

[michel123456]

well, I think the vector would be the same size as all the others on the red circle. Maybe this would be a good way of looking at it,

 

 

So that all of the red lines are the same size, the ones where the tangent is the line of expansion too. It's important also that the lengths are proportional, so for example AB/AD is equal to AC/AE and AF/AG since velocity from the center needs to be proportional to distance.

 

I'm pretty sure the standard wisdom is that this checks out.

 

[edited for having proportional lengths transposed]

 

Your skecth represents a scaling factor. Now i realize you & Icarus2 must be correct, and I must be wrong in posts #4 & 15 since the OP sketch represents a scaling factor too.

Interesting way to link acceleration with scaling.

Edited September 24, 2012 by michel123456

[icarus2]

How can the universe expand if space is not expanding

Dear StringJunky,

I am sorry. I apologize for my poor English.

 

After accelerating expansion(such as inflation) of early universe has almost finished, particles started to have some velocity.

 

This velocity distribution naturally has higher velocity when it is further away from the center of the universe and has lower velocity when it is closer to the center.

 

A. Big bang simulation in the zero energy universe

refer time : 9m:16s ~

 

Fig14. m+=+1 (1,000ea), -m-=-1 (1,000ea),

U++ = -5190.4707907,

U-- = -5308.0373689,

U-+= +10499.2712222,

U_tot = 0.7630625

 

Total rest mass energy is zero. Total gravitational potential energy is +0.763.

 

[math]|\frac{{{U_{tot}}}}{{{U_{ - + }}}}| = 0.0000726[/math]. Thus, U_tot is almost zero.

 

We could not make GPE 0 for there were too many particles. Therefore, we simulated dividing the value of U_tot(total GPE) into two parts which are when it is little bit bigger than 0 (+0.76306) and when smaller than 0 (-0.53277), and we could gain almost similar results.

 

 

B. Accelerating expansion of the universe (such as inflation)

 

It can be confirmed that even though the total energy starts with 0, the universe expands and positive masses combine one another due to attractive interaction among themselves, while negative masses cannot form massive mass structure because of repulsive interaction.

 

In the Zero Energy Universe, even if the total energy and total gravitational potential energy are 0, the universe can expand in acceleration.

 

 

How can preserve isotropy and homogeneity (or don't you think so?)?

 

In my opinion, I doubt (almost perfact)) isotropy and homogeneity at the whole universe.

Universe is very big, so we can observe isotropy and homogeneity at scale of a few 100MPC. But, if we can observe the whole universe, we could observe both isotropy and anisotropy.

 

I doubt that 2.7K background radiation(CMBR) is radiation in the early days of the universe

 

 

Wow! It’s perfect. Beautiful results, 10000%. However, if we considering that 2.7K background radiation(CMBR) is 3000K radiation in the early days of the universe, namely age of CMBR is about 13.7Gy. Length of path of CMBR is about 13.7Gly. On path of CMBR, numerous galaxy and heat source are existed. Of course, I know that WMAP image of CMB temperature anisotropy.

 

It is too perfect, too clean, too beautiful result. Therefore, I doubt it.

There is a possibility that 2.7K background radiation is not radiation in the early days of the universe. In that case, we can't estimate that our universe is isotropic and uniform from CMBR. Of course, other possibilities also existed.

 

if redshifting galaxies are accepted, they can't physically move at superluminal speeds (Re: SR), so, space expansion is the only other option or do you assert physical objects can move FTL into a pre-existing space?

 

Due to “model of expansion of space” distant objects can receding faster than c.

But, in my model, they can't physically move at superluminal speeds.

 

Is what problem?

In my opinion, problem is wrong relation eq. (R=1/(1+z))

We don’t know velocity of distant galaxy. We don’t observe velocity of distant galaxy. We observe only redshift and then, we estimate the scale factor, velocity, distance….

 

Key point of problem, R=1/(1+z), it is derived from assumption which space does expand.

 

If space does not expand, R=1/(1+z) is wrong. Therefore, existing velocity and distance value of distant galaxy are also wrong.

 

When space doesn't expand, the maximum value of recession velocity will become light velocity c.

 

Have a nice day!

 

--- Icarus2

Edited September 24, 2012 by icarus2

[Iggy]

Is what problem?

In my opinion, problem is wrong relation eq. (R=1/(1+z))

We don’t know velocity of distant galaxy. We don’t observe velocity of distant galaxy. We observe only redshift and then, we estimate the scale factor, velocity, distance….

 

Key point of problem, R=1/(1+z), it is derived from assumption which space does expand.

 

If space does not expand, R=1/(1+z) is wrong. Therefore, existing velocity and distance value of distant galaxy are also wrong.

 

When space doesn't expand, the maximum value of recession velocity will become light velocity c.

Icarus, I believe you would benefit from reading the following links. I'll quote a part of each,

 

Are galaxies really moving away from us or is space just expanding?

 

This depends on how you measure things, or your choice of coordinates. In one view, the spatial positions of galaxies are changing, and this causes the redshift. In another view, the galaxies are at fixed coordinates, but the distance between fixed points increases with time, and this causes the redshift. General relativity explains how to transform from one view to the other, and the observable effects like the redshift are the same in both views. Part 3 of the tutorial shows space-time diagrams for the Universe drawn in both ways.

 

Frequently Asked Questions in Cosmology

 

What Causes the Hubble Redshift? Are the light waves "stretched" as the universe expands, or is the light doppler-shifted because distant galaxies are moving away from us?

 

In a word: yes. In two sentences: the Doppler shift explanation is a linear approximation to the "stretched light" explanation. Switching from one viewpoint to the other amounts to a change of coordinate systems in (curved) spacetime.

 

Michael Weiss Physics FAQ

 

The space-time diagram below shows a "zero" (really very low) density cosmological model plotted using the D_NOW and t of the Hubble law... In these variables, velocities greater than c are certainly possible, and since the open Universes are spatially infinite, they are actually required. But there is no contradiction with the special relativistic principle that objects do not travel faster than the speed of light, because if we plot exactly the same space-time in the special relativistic x and t coordinates we get:

 

<...>

 

...in special relativistic (x and t) coordinates the velocities are less than c.... The relationships between the Hubble law distance and velocity (D_NOW & v) and the redshift z are given below:

 

v = H₀D_NOW

D_NOW = (c/H₀)ln(1+z)

1+z = exp(v/c)

 

Ned Wright Tutorial Part 2

If you start with static coordinates and assume that galaxies are moving through space you will get different formula from starting with comoving coordinates and assuming that space is expanding. They are different formula because the variables mean different things in each. It isn't an error, it is just a different way of looking at things. Comoving coordinates are a much easier, more exacting, and more natural way of solving expansion.