Wednesday, November 19, 2014

Another argument against the BBT

In The Equivalence Principle and the Big Bang Theory, we explored the idea that the galaxies are exhibiting a redshift that can be interpreted either as a Doppler effect, that is, they are moving away, or as a gravitational shift, in which case we can safely say they are at rest with each other. An argument for the BBT that every observer in the universe will see every other galaxy moving away is often used to validate the BBT. This argument is misleading. It is only partially true if one ignores that velocity has not only magnitude but it has also a direction.



According to an observer in our galaxy, he sees every other galaxy moving away. (Black Arrows). However, an observer from another galaxy, say the blue one, sees the other galaxies moving away but in different directions than what we see (Blue Arrows).



We will agree with her concerning both of our galaxies - She sees us move away from her, we see her moving away from us along the same line, and since motion is relative, our observation agrees. However, we will disagree about the direction for galaxies Red, Green and any other galaxy not situated along the line joining our two galaxies.

On the other hand, if we agree that instead of a Doppler shift, the galaxies are exhibiting a gravitational shift and are at rest with each other, then we all agree that the net force on any galaxy is zero.



Cosmic Microwave Background

The last remaining argument in favor of the BBT is the Cosmic Microwave Background (CMB). It has been said that only a Hot Big Bang scenario can explain the CMB, and any other explanation would have to be contrived. In future blogs, I will demonstrate that the explanation of the CMB from a Hot Big Bang scenario is itself contrived. Stay tuned.

Saturday, November 01, 2014

The Equivalence Principle and the Big Bang Theory

In this blog I explore the idea that Hubble failed to notice an important aspect of Einstein’s Equivalence Principle.

Consider this thought experiment. Different emitters are placed at different heights from the ground. The earth plays the role of the source of gravity.



They emit light, which from an earth observer, would be blueshifted. According to Einstein’s Equivalence Principle: we can say that the Doppler effect is equal to the gravitational shift ( see equation 2 in The Essential General Relativity , reproduced below)

(1) (Δf/f)gravity = -(Δf/f)doppler = -Δv/c

For emitter 1, we can say,

(2) Δv1 = g(d1) Δt1 (definition of acceleration, where g(d1) is the gravitational potential field at d1.

(3) Define g(d1) = g1

(4) Δv1 = g1 (d1/c) (time = distance/velocity)

(5) However, g1 = (GMsource)/ R21
= (GMsource)/ (Rsource + d1)2
= (GMsource) (Rsource + d1)−2
= (GMsource/ R2source) ( 1 + d1 / Rsource)−2
≈ (GMsource/ R2source) ( 1 − 2d1 / Rsource)
For 2d1 << Rsource

(6) g1 = (GMsource)/ R2source

Substitute (6) into (4),

(7) Δv1 = (GMsource)/ cR2source )(d1)

We can get the same result for emitters 2 and 3,

(8) Δv2 = (GMsource)/ cR2source )(d2)

(9) Δv3 = (GMsource)/ cR2source )(d3)

We can generalize equations 7,8 and 9 as,

(10) Δv = Hd ,

where H = (GMsource)/ (cR2source)

In case you haven’t recognized this, it is Hubble’s equation. When he discovered that all galaxies have a redshifted spectrum, Hubble concluded that all the galaxies were moving away. That is the Doppler Effect. However using Einstein’s Equivalence Principle, we can say that galaxies are at rest, and photons are redshifted( they are moving against gravity). Note that Hubble discovered not a change in velocity but just a velocity. In his days, he did not have the technology to observe such a small change in the galaxies' velocities, and it took nearly 70 years before it was discovered that galaxies are actually accelerating.

In our thought experiment, the emitters are at rest, so one can easily say that such emitters would start to accelerate as they cannot be “nailed” in outer space. What about the galaxies, can they be “nailed” so that we can claim they are at rest with respect to each other? Consider one galaxy against all others.



According to Gauss’ theorem (see fig.3 in Newton's Law of Gravity), a galaxy would be attracted as if all the matter inside the sphere were concentrated at the center of that sphere. One can ignore all the other galaxies outside that sphere. At the same time, one can draw an infinite number of spheres, in which the galaxy would be attracted to the center of each sphere. Here’s a diagram with just three spheres drawn.



If the universe is infinite, we can safely say that the total force on a galaxy is zero, and therefore, the galaxies are nearly at rest.



Does it mean that the Big Bang theory is wrong? No. The Big Bang theory says that for every galaxy, all other galaxies are moving away. But Einstein’s Equivalence Principle also says that we can look at every galaxy at rest with their light being redshifted. Both pictures are equivalent.



APPENDIX

Equation 10 is true for every galaxy, since each one is emitting light from a source of gravity that has an infinite radius. This argument is only valid if the universe is infinite.