# Help Us Stay Informed on Mainstream Cosmology

Discussion in 'Astronomy, Exobiology, & Cosmology' started by danshawen, Nov 18, 2015.

1. ### rpennerFully WiredValued Senior Member

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Your distinction is one without meaning.

You seem to be objecting to my results because the choice to use SI units requires that I insert factors with the units of velocities in order to make the terms on either side of the minus sign have the same units and that the physical evidence requires that I always choose "c" as that factor. In choices of units where "c=1" those same invariants can be written omitting the factors of c but without changing the physical claim.

Demonstration that the speed of light is invariant under Lorentz transforms can be shown for a special case of showing $c^2 \left( \Delta t_{AB} \right)^2 \; - \; \left( \vec{x}_{AB} \right)^2$ is invariant under Lorentz transformations which follows that $c^2 \, \Delta t_{AB} \, \Delta t_{CD} \; - \; \vec{x}_{AB} \, \cdot \, \vec{x}_{CD}$ is invariant under Lorentz transforms which were established as the relations between two equally valid systems of inertial coordinates from Einstein's twin postulates that the speed of light is independent of its source and that any choice of coordinates where the law of inertia applies is a good choice.

Einstein's choices mean space and time are aspects of the same geometrical system and just like rotation can blend x and y into new combination, so can Lorentz transforms blend time and space. But just like rotations holds the length of line segments (and the value of the dot-product) invariant under the rotation transformation, so the Lorentz transforms preserve the space-time interval (and the space-time dot product).

We can use matrices to show this space-time dot product can be viewed as a triple product.
$c^2 \, \Delta t_{AB} \, \Delta t_{CD} \; - \; \vec{x}_{AB} \, \cdot \, \vec{x}_{CD} = \begin{pmatrix} c \Delta t_{AB} \\ \Delta x_{AB} \\ \Delta y_{AB} \\ \Delta z_{AB} \end{pmatrix}^T \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix} \begin{pmatrix} c \Delta t_{CD} \\ \Delta x_{CD} \\ \Delta y_{CD} \\ \Delta z_{CD} \end{pmatrix}$
Matrices also allow use to write arbitrary linear transforms:
$\begin{pmatrix} c \Delta t' \\ \Delta x' \\ \Delta y' \\ \Delta z' \end{pmatrix} = \Lambda \; \begin{pmatrix} c \Delta t \\ \Delta x \\ \Delta y \\ \Delta z \end{pmatrix}$

While the X-direction Lorentz transform is generally written as one of the following:
$\Lambda = \begin{pmatrix} \frac{1}{\sqrt{1 - \frac{u^2}{c^2}}} & \frac{u}{c} \frac{1}{\sqrt{1 - \frac{u^2}{c^2}}} & 0 & 0 \\ \frac{u}{c} \frac{1}{\sqrt{1 - \frac{u^2}{c^2}}} & \frac{1}{\sqrt{1 - \frac{u^2}{c^2}}} & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix} = \begin{pmatrix} \cosh \, \rho & \sinh \, \rho & 0 & 0 \\ \sinh \, \rho & \cosh \, \rho & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix} = \textrm{exp} \, \begin{pmatrix} 0 & \rho & 0 & 0 \\ \rho & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{pmatrix}$
which is nice because $\Lambda^T = \Lambda$, we may also use the more general form:
$\Lambda = \textrm{exp} \, \begin{pmatrix} 0 & \rho_x & \rho_y & \rho_z \\ \rho_x & 0 & \theta_z & - \theta_y \\ \rho_y & -\theta_z & 0 & \theta_x \\ \rho_z & \theta_y & -\theta_x & 0 \end{pmatrix}$
where for any square matrix, M, we have
$\textrm{exp} \, M = \sum_{k=0}^{\infty} \frac{1}{k!} M^k = I + \sum_{k=1}^{\infty} \frac{1}{k!} M^k$
from which it follows that
$\left( \textrm{exp} \, M \right)^T = \textrm{exp} \, M^T$.
In this more general Lorentz transform, $\Lambda^T = \Lambda$ is not always true.

So
$\Lambda^T \; \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix} \; \Lambda \\ = \left( \sum_{j=0}^{\infty} \frac{1}{j!} \begin{pmatrix} 0 & \rho_x & \rho_y & \rho_z \\ \rho_x & 0 & -\theta_z & \theta_y \\ \rho_y & \theta_z & 0 & -\theta_x \\ \rho_z & -\theta_y & \theta_x & 0 \end{pmatrix}^j \right) \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix} \left( \sum_{k=0}^{\infty} \frac{1}{k!} \begin{pmatrix} 0 & \rho_x & \rho_y & \rho_z \\ \rho_x & 0 & \theta_z & - \theta_y \\ \rho_y & -\theta_z & 0 & \theta_x \\ \rho_z & \theta_y & -\theta_x & 0 \end{pmatrix}^k \right) \\ = \sum_{n=0}^{\infty} \sum_{i=0}^{n} \frac{1}{i! (n-i)!} \begin{pmatrix} 0 & \rho_x & \rho_y & \rho_z \\ \rho_x & 0 & -\theta_z & \theta_y \\ \rho_y & \theta_z & 0 & -\theta_x \\ \rho_z & -\theta_y & \theta_x & 0 \end{pmatrix}^i \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix} \begin{pmatrix} 0 & \rho_x & \rho_y & \rho_z \\ \rho_x & 0 & \theta_z & - \theta_y \\ \rho_y & -\theta_z & 0 & \theta_x \\ \rho_z & \theta_y & -\theta_x & 0 \end{pmatrix}^{n-i} \\ = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix} \\ \quad + \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix} \begin{pmatrix} 0 & \rho_x & \rho_y & \rho_z \\ \rho_x & 0 & \theta_z & - \theta_y \\ \rho_y & -\theta_z & 0 & \theta_x \\ \rho_z & \theta_y & -\theta_x & 0 \end{pmatrix} + \begin{pmatrix} 0 & \rho_x & \rho_y & \rho_z \\ \rho_x & 0 & -\theta_z & \theta_y \\ \rho_y & \theta_z & 0 & -\theta_x \\ \rho_z & -\theta_y & \theta_x & 0 \end{pmatrix} \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix} \\ \quad + \frac{1}{2} \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix} \begin{pmatrix} 0 & \rho_x & \rho_y & \rho_z \\ \rho_x & 0 & \theta_z & - \theta_y \\ \rho_y & -\theta_z & 0 & \theta_x \\ \rho_z & \theta_y & -\theta_x & 0 \end{pmatrix}^2 + \begin{pmatrix} 0 & \rho_x & \rho_y & \rho_z \\ \rho_x & 0 & -\theta_z & \theta_y \\ \rho_y & \theta_z & 0 & -\theta_x \\ \rho_z & -\theta_y & \theta_x & 0 \end{pmatrix} \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix} \begin{pmatrix} 0 & \rho_x & \rho_y & \rho_z \\ \rho_x & 0 & \theta_z & - \theta_y \\ \rho_y & -\theta_z & 0 & \theta_x \\ \rho_z & \theta_y & -\theta_x & 0 \end{pmatrix} + \frac{1}{2} \begin{pmatrix} 0 & \rho_x & \rho_y & \rho_z \\ \rho_x & 0 & -\theta_z & \theta_y \\ \rho_y & \theta_z & 0 & -\theta_x \\ \rho_z & -\theta_y & \theta_x & 0 \end{pmatrix}^2 \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix} \\ \quad + \sum_{n=3}^{\infty} \sum_{i=0}^{n} \frac{1}{i! (n-i)!} \begin{pmatrix} 0 & \rho_x & \rho_y & \rho_z \\ \rho_x & 0 & -\theta_z & \theta_y \\ \rho_y & \theta_z & 0 & -\theta_x \\ \rho_z & -\theta_y & \theta_x & 0 \end{pmatrix}^i \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix} \begin{pmatrix} 0 & \rho_x & \rho_y & \rho_z \\ \rho_x & 0 & \theta_z & - \theta_y \\ \rho_y & -\theta_z & 0 & \theta_x \\ \rho_z & \theta_y & -\theta_x & 0 \end{pmatrix}^{n-i} \\ = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix}$

So we have:
$c^2 \, \Delta t'_{AB} \, \Delta t'_{CD} \; - \; \vec{x}'_{AB} \, \cdot \, \vec{x}'_{CD} \\ = \left( \Lambda \; \begin{pmatrix} c \Delta t_{AB} \\ \Delta x_{AB} \\ \Delta y_{AB} \\ \Delta z_{AB} \end{pmatrix} \right) ^T \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix} \left( \Lambda \; \begin{pmatrix} c \Delta t_{CD} \\ \Delta x_{CD} \\ \Delta y_{CD} \\ \Delta z_{CD} \end{pmatrix} \right) \\ = \begin{pmatrix} c \Delta t_{AB} \\ \Delta x_{AB} \\ \Delta y_{AB} \\ \Delta z_{AB} \end{pmatrix}^T \left( \Lambda^T \; \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix} \; \Lambda \right) \begin{pmatrix} c \Delta t_{CD} \\ \Delta x_{CD} \\ \Delta y_{CD} \\ \Delta z_{CD} \end{pmatrix} \\ = \begin{pmatrix} c \Delta t_{AB} \\ \Delta x_{AB} \\ \Delta y_{AB} \\ \Delta z_{AB} \end{pmatrix}^T \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix} \begin{pmatrix} c \Delta t_{CD} \\ \Delta x_{CD} \\ \Delta y_{CD} \\ \Delta z_{CD} \end{pmatrix} \\ = c^2 \, \Delta t_{AB} \, \Delta t_{CD} \; - \; \vec{x}_{AB} \, \cdot \, \vec{x}_{CD}$
which proves the invariant from the general Lorentz transforms.

Last edited: Nov 23, 2015
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3. ### rpennerFully WiredValued Senior Member

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Hit the 10k character limit.

$\begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix} \begin{pmatrix} 0 & \rho_x & \rho_y & \rho_z \\ \rho_x & 0 & \theta_z & - \theta_y \\ \rho_y & -\theta_z & 0 & \theta_x \\ \rho_z & \theta_y & -\theta_x & 0 \end{pmatrix} + \begin{pmatrix} 0 & \rho_x & \rho_y & \rho_z \\ \rho_x & 0 & -\theta_z & \theta_y \\ \rho_y & \theta_z & 0 & -\theta_x \\ \rho_z & -\theta_y & \theta_x & 0 \end{pmatrix} \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix} \\ = \begin{pmatrix} 0 & \rho_x & \rho_y & \rho_z \\ -\rho_x & 0 & -\theta_z & \theta_y \\ -\rho_y & \theta_z & 0 & -\theta_x \\ -\rho_z & -\theta_y & \theta_x & 0 \end{pmatrix} + \begin{pmatrix} 0 & -\rho_x & -\rho_y & -\rho_z \\ \rho_x & 0 & \theta_z & -\theta_y \\ \rho_y & -\theta_z & 0 & \theta_x \\ \rho_z & \theta_y & -\theta_x & 0 \end{pmatrix} \\ = \begin{pmatrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{pmatrix} \\ = 0$

$\frac{1}{2} \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix} \begin{pmatrix} 0 & \rho_x & \rho_y & \rho_z \\ \rho_x & 0 & \theta_z & - \theta_y \\ \rho_y & -\theta_z & 0 & \theta_x \\ \rho_z & \theta_y & -\theta_x & 0 \end{pmatrix}^2 + \begin{pmatrix} 0 & \rho_x & \rho_y & \rho_z \\ \rho_x & 0 & -\theta_z & \theta_y \\ \rho_y & \theta_z & 0 & -\theta_x \\ \rho_z & -\theta_y & \theta_x & 0 \end{pmatrix} \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix} \begin{pmatrix} 0 & \rho_x & \rho_y & \rho_z \\ \rho_x & 0 & \theta_z & - \theta_y \\ \rho_y & -\theta_z & 0 & \theta_x \\ \rho_z & \theta_y & -\theta_x & 0 \end{pmatrix} + \frac{1}{2} \begin{pmatrix} 0 & \rho_x & \rho_y & \rho_z \\ \rho_x & 0 & -\theta_z & \theta_y \\ \rho_y & \theta_z & 0 & -\theta_x \\ \rho_z & -\theta_y & \theta_x & 0 \end{pmatrix}^2 \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix} \\ = \frac{1}{2} \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix} \begin{pmatrix} \rho_x^2 + \rho_y^2 + \rho_z^2 & \theta_y \rho_z - \rho_y \theta_z & \rho_x \theta_z - \theta_x \rho_z & \theta_x \rho_y - \rho_x \theta_y \\ \rho_y \theta_z - \theta_y \rho_z & \rho_x^2 - \theta_y^2 - \theta_z^2 & \rho_x \rho_y + \theta_x \theta y & \rho_x \rho_z + \theta_x \theta_z \\ \theta_x \rho_z - \rho_x \theta_z & \rho_x \rho_y + \theta_x \theta y & - \theta_x^2 + \rho_y^2 - \theta_z^2 & \rho_y \rho_z + \theta_y \theta_z \\ \rho_x \theta_y - \theta_x \rho_y & \rho_x \rho_z + \theta_x \theta_z & \rho_y \rho_z + \theta_y \theta_z & -\theta_x^2 -\theta_y^2 + \rho_z^2 \end{pmatrix} + \begin{pmatrix} 0 & \rho_x & \rho_y & \rho_z \\ \rho_x & 0 & -\theta_z & \theta_y \\ \rho_y & \theta_z & 0 & -\theta_x \\ \rho_z & -\theta_y & \theta_x & 0 \end{pmatrix} \begin{pmatrix} 0 & \rho_x & \rho_y & \rho_z \\ -\rho_x & 0 & -\theta_z & \theta_y \\ -\rho_y & \theta_z & 0 & -\theta_x \\ -\rho_z & -\theta_y & \theta_x & 0 \end{pmatrix} + \frac{1}{2} \begin{pmatrix} \rho_x^2 + \rho_y^2 + \rho_z^2 & \rho_y \theta_z - \theta_y \rho_z & \theta_x \rho_z - \rho_x \theta_z & \rho_x \theta_y - \theta_x \rho_y \\ \theta_y \rho_z - \rho_y \theta_z & \rho_x^2 - \theta_y^2 - \theta_z^2 & \rho_x \rho_y + \theta_x \theta y & \rho_x \rho_z + \theta_x \theta_z \\ \rho_x \theta_z - \theta_x \rho_z & \rho_x \rho_y + \theta_x \theta y & - \theta_x^2 + \rho_y^2 - \theta_z^2 & \rho_y \rho_z + \theta_y \theta_z \\ \theta_x \rho_y - \rho_x \theta_y & \rho_x \rho_z + \theta_x \theta_z & \rho_y \rho_z + \theta_y \theta_z & -\theta_x^2 -\theta_y^2 + \rho_z^2 \end{pmatrix} \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix} \\ = \frac{1}{2} \begin{pmatrix} \rho_x^2 + \rho_y^2 + \rho_z^2 & \theta_y \rho_z - \rho_y \theta_z & \rho_x \theta_z - \theta_x \rho_z & \theta_x \rho_y - \rho_x \theta_y \\ \theta_y \rho_z - \rho_y \theta_z & - \rho_x^2 + \theta_y^2 + \theta_z^2 & - \rho_x \rho_y - \theta_x \theta y & - \rho_x \rho_z - \theta_x \theta_z \\ \rho_x \theta_z - \theta_x \rho_z & - \rho_x \rho_y - \theta_x \theta y & \theta_x^2 - \rho_y^2 + \theta_z^2 & - \rho_y \rho_z - \theta_y \theta_z \\ \theta_x \rho_y - \rho_x \theta_y & - \rho_x \rho_z - \theta_x \theta_z & - \rho_y \rho_z - \theta_y \theta_z & \theta_x^2 + \theta_y^2 - \rho_z^2 \end{pmatrix} + \begin{pmatrix} -\rho_x^2 - \rho_y^2 - \rho_z^2 & \rho_y \theta_z - \theta_y \rho_z & \theta_x \rho_z - \rho_x \theta_z & \rho_x \theta_y - \theta_x \rho_y\\ \rho_y \theta_z - \theta_y \rho_z & \rho_x^2 - \theta_y^2 - \theta_z^2 & \rho_x \rho_y + \theta_x \theta y & \rho_x \rho_z + \theta_x \theta_z \\ \theta_x \rho_z - \rho_x \theta_z & \rho_x \rho_y + \theta_x \theta y & - \theta_x^2 + \rho_y^2 - \theta_z^2 & \rho_y \rho_z + \theta_y \theta_z \\ \rho_x \theta_y - \theta_x \rho_y & \rho_x \rho_z + \theta_x \theta_z & \rho_y \rho_z + \theta_y \theta_z & - \theta_x^2 - \theta_y^2 + \rho_z^2 \end{pmatrix} + \frac{1}{2} \begin{pmatrix} \rho_x^2 + \rho_y^2 + \rho_z^2 & \theta_y \rho_z - \rho_y \theta_z & \rho_x \theta_z - \theta_x \rho_z & \theta_x \rho_y - \rho_x \theta_y \\ \theta_y \rho_z - \rho_y \theta_z & - \rho_x^2 + \theta_y^2 + \theta_z^2 & - \rho_x \rho_y - \theta_x \theta y & - \rho_x \rho_z - \theta_x \theta_z \\ \rho_x \theta_z - \theta_x \rho_z & - \rho_x \rho_y - \theta_x \theta y & \theta_x^2 - \rho_y^2 + \theta_z^2 & - \rho_y \rho_z - \theta_y \theta_z \\ \theta_x \rho_y - \rho_x \theta_y & - \rho_x \rho_z - \theta_x \theta_z & - \rho_y \rho_z - \theta_y \theta_z & \theta_x^2 + \theta_y^2 - \rho_z^2 \end{pmatrix} \\ = 0$

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5. ### brucepValued Senior Member

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4,098
The reason Steinhardt slams cosmic inflation is because he has a competing theory which is somewhat ignored. That's my opinion. He's running his mouth in favor of his idea and throwing cosmic inflation under the bus. You should learn some details about both theories then your comments might be worth listening to.

Last edited: Nov 23, 2015

7. ### dumbest man on earthReal Eyes Realize Real LiesValued Senior Member

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brucep, you haven't the foggiest idea of the extent of my knowledge on these "theories"...

at any rate...you are only contradicting yourself...
my "comments" must be "worth listening to"...(or worth reading, at least), or you would not have 'Trolled' my Post...

BTW: it is Theoretical Science...is it not?

8. ### danshawenValued Senior Member

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3,950
I understand perfectly. It's wrong. It isn't that the math itself is wrong. Matrices are fine for analyzing structures of all types, even to a considerable extent, atomic structure.

But is wrong to use Euclidean geometry to analyze energy exchanges in relativistic space. Vectors representing velocities don't work there, or if they do, in a very limited sense. Hyperbolic transforms of vectors don't capture features of relativistic space we already know are true. The ideas of Minkowski required a great deal more sweeping assumptions about Lorentz covariance that Einstein's original vision did not. There was never any indication by any experiment in physics that suggested a Pythagorean covariance between space and time. Yes, I know the protons in the rings of the LHC would observe the whole extent of the ring to be about 12 meters in length or even less now that the upgrades are completed. But spatial covariance geometry is not needed at all, even here, and the best concept is to dispense with is space. It isn't "space". It's light travel TIME. It's Doppler shifts, even in bound energy NOT length contraction. Space doesn't warp around gravitating objects. Time dilates, and there is a good reason for that. It dilates because bound energy interacts with the Higgs field. The protons in the LHC interact with Higgs all the way to the collision detectors. It's the reason you can pump as much energy as you wish into them. Time continues to dilate the more energy you pump into them, doesn't it? Throw away the rubber sheets and stow them with Hooke's spring and clockwork universe. Space doesn't warp; time dilates. Higgs is what makes it dilate. I have explained how that occurs.

And Lorentz covariance isn't going to explain the first thing about what it means for bound energy in relativistic geometry to obtain inertia, much less what entanglement really means. Covariance isn't needed. We don't CARE what "space" does. It doesn't matter one way or the other.

QCD already failed to produce a calculation for the spin of a proton using these techniques. Physics isn't going to go any further until or unless the tethers to an obsoleted spatial geometry are permanently cut. Time dilation is all you need to understand in a universe that is comprised of energy transfer events.

Last edited: Nov 24, 2015
9. ### rpennerFully WiredValued Senior Member

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Pardon, but what? Where do I use Euclidean geometry?

I'm not transforming 3-vectors of 3-dimensional Euclidean geometry, but 4-vectors of (3,1) Lorentzian space-time which are compose of a time interval and a 3-dimental spatial interval.

10. ### danshawenValued Senior Member

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3,950
Whenever you use a "Lorentz transform", you do so with the understanding that it operates on a coordinate system in a EUCLIDEAN space that has a FIXED ORIGIN in SPACE as a reference.

Don't forget, my freshman physics prof at the University of Maryland in 1970 wasted hours upon hours of class time presenting us his own personal derivation of Lorentz transformations, starting with raw coordinate systems in different inertial reference frames. I read it over and over again for years, even a few times after I received my bachelors degree in physics. It was rubbish for a different reason, but his derivation was close enough to a genuine one I found later to determine that ANY COORDINATE SYSTEM OR GEOMETRY FOR INERTIALESS RELATIVISTIC SPACE WHICH REQUIRES AN ORIGIN is invalid in any setting other than a large chunk of Euclidean solid AT REST. The only absolute space in this universe is at the exact centers of particles of bound energy. All energy exchange events in this universe take place limited by the speed of light in the case of unbound energy, and rotation with no passage of time for bound energy. QFT's assertion that particles have no SPATIAL dimensions is pretty useless, but you will find that thinking of the rotation inside bound energy taking place with no passage of time (until interaction with the Higgs mechanism) is a concept that explains much, much more.

That freshman professor of mine died five years ago without publishing anything substantive in physics or anything else. Good riddance. He FAILED me, and I am actually proud of that. At least, we won't have another Einstein-Minkowski-Hilbert triad with what I am telling you.

The Higgs field gives a reason for Special Relativity that Einstein's original description lacked. There is good reason why time dilates when bound matter is accelerated, and why the same thing happens surrounding gravitating objects, or for that matter, any atom or beam of photons. The Higgs field is Einstein's unseen second observer for every energy transfer event in this universe. Every time there is a change of inertial reference frame or energy, acceleration relative to the Higgs field and with respect to the way it interacts with all other particles of bound energy in other reference frames in the universe is involved. And all of these clocks run at different rates and affect the rates of other clocks as they change. I hope you don't expect me to complete all of the math that goes with this. I didn't create the homework problem. The LHC did.

And now that I understand this, I really could care less about Ancient Greek geometry. Have at it all you wish. Eventually, it will be relegated to the learning status of Roman Numerals for multiplication. The Pythagorean theorem requires AN ORIGIN. Too bad, there really aren't any that can be relied upon to do Euclidean geometry in relativistic space. Orient any right triangle so that the plane is vertical near the surface of the Earth. Guess what? It isn't a triangle any more. The sides aren't straight any more, and time dilates so that it runs slower at the lower end. And if, like Minkowski, you believe that tossing in complex numbers is going to fix your geometry so that it works like it does in a solid, well, good luck with that..

Last edited: Nov 24, 2015

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27,534
Spot on brucep...While I like the idea of a cyclic universe, we have absolutely no evidence for such and it really explains nothing better than the speculation of a "Universe being the ultimate free lunch" by Professor's Filippenko and Pasachoff, https://www.astrosociety.org/publications/a-universe-from-nothing/ and/or "the universe from nothing"by Laurence Krauss.
Inflation on the other hand, although lacking direct observational evidence, has heaps going for it, in the precise way it explains for anomalies of the BB, like homogeneity and Isotropy.
http://www.counterbalance.org/cq-guth/evide-frame.html
Phil Plaitt I believe sums it up nicely.........
"The bottom line is that they do still see some evidence for gravitational waves affecting the light from the early Universe, but it doesn’t look like it rises to being statistically significant, and it’s certainly not as strong as they first thought.

In other words, they cannot say if they have direct evidence for inflation or not. The new results neither prove nor disprove inflation. They’re inconclusive. The observations may all be the result of dust in our galaxy, or it may be that there is some excess signal caused by inflation. Given the current data, we just can’t say".

::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Failure?? Far from it......What BICEP2 did do is show how science/cosmology is self correcting, within mainstream circles and without any hindrance one way or the other from those "cocky's on the biscuit tin" [they just ain't in it]that frequent forums such as this sprouting their collective nonsense.
Still, where else have they got to go?
It's just going to take a little bit longer...Let's all hope that these justified important experiments continue.

Cyclic universes, parallel universes, free lunches, etc although all speculatively interesting, must remain in that realm at this stage.

12. ### brucepValued Senior Member

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4,098
To be fair Steinhardt's new version of the ekpyrotic cosmology hasn't been falsified. I think if BCP2 results were what was predicted the ekpyrotic model would have been falsified.

13. ### dumbest man on earthReal Eyes Realize Real LiesValued Senior Member

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3,522

Like I said when I first thanked Farsight for Linking it...the article is a great, quick read for anyone honestly interested in the current state of Theoretical Physics in relation to "Inflation"!
http://blogs.scientificamerican.com/cross-check/physicist-slams-cosmic-theory-he-helped-conceive/

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Yep, Professor Steinhardt basically said the same.
He makes a couple of good points, but certainly not enough to invalidate any Inflation epoch and the questions which it answers and anomalies which it solves.

15. ### rpennerFully WiredValued Senior Member

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1) That's not the definition of Euclidean. That's the definition of Cartesian coordinates.
2) I eliminate any possible dependence on the choice of origin by working with coordinate differences. That works because the Lorentz transformation is linear in the coordinates.

danshawen likes this.
16. ### brucepValued Senior Member

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No disrespect intended the ekpyrotic was saved by the dust. It also doesn't predict a multi verse. Check this one out.
http://arxiv.org/abs/1510.00126
The analysis has a 30% error bar. Pretty esoteric stuff.

danshawen likes this.

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Yes, exactly.....
In a exchange with our illustrious Schmelzer, I told him earlier that from the link itself, Steinhardt said himself, that any verification of gravity waves would invalidate the cyclic model.
http://blogs.scientificamerican.com/cross-check/physicist-slams-cosmic-theory-he-helped-conceive/
All I said was that we already have reasonably considered indirect evidence for gravity waves.
I don't believe that the BB will be surpassed any time soon.

18. ### brucepValued Senior Member

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I'm pretty sure the way he meant that is during the origin event no primordial [whatever that means] gravitational waves are predicted to be generated.

19. ### SchmelzerValued Senior Member

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No, this is only how you have distorted Steinhardt's claim, which is:
Do you at least understand that there is a difference between "detectable primordial" gravitational waves and simply gravitational waves?

Last edited: Nov 24, 2015
20. ### The GodValued Senior Member

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You beat me to that. In fact I was having a hearty laugh how this character Paddoboy swinged based on Brucep posts...

I am seeing a good amount of change in Brucep's posts, he has started seeing Paddoboy's posts critically.....Possibly he has waited enough and when found no improvement in Paddoboy, he took up the task to educate him.

21. ### danshawenValued Senior Member

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Time isn't the FOURTH dimension, mangled by a mathematician's fevered dreams about Euclidean, Pythagorean, or complex geometry or intervals or any combination of those. Time is, literally EVERY dimension, all the way out to 13.7 light years and beyond IN EVERY DIRECTION we can see, illuminated by propagating unbound virtual energy and whatever other energy exchange events are occurring that far out, for as far as it goes.

The physics professor who failed me was Daniel Fivel. I received an A+ in the same physics course from Dr. Richard Prange (who has a memorial foundation trust in his name) the following semester with virtually no additional study, other than his excellent lectures.

It was a much different and a better experience, and I even talked to Dr. Prange again at a colloquia two years prior to his death, many years earlier than Fivel. I told him about our pioneering work in the DARPA Grand Challenge 2005 as I recall. I miss him very much.

Happy Thanksgiving, rpenner. Peace.

I'm assuming you understand my 2D triangle thought experiment at the surface of the Earth. It's the simplest one I can think of to show the folly of an argument that time dilation is hyperdimensional somehow.

When a "perfect" Euclidean 1 meter solid right triangle shape is fabricated out of any material, orienting the plane of the triangle vertically with the base down means that the two vertical sides of the triangle will trace exactly the same geometry that two laser beams for sides would. They would bend as thought they were accelerating at 9.8 meters per second per second. The base of the triangle, the lowest part of it, is where TIME DILATES so that it runs slower than it does at the top. No fourth dimensional geometry is necessary to understand that it does this, or even the reason that it does this.

I understand that you are under contractual requirements and other legal instruments that prevent you from commenting on all of my statements. It's fine. As long as you understand, that's really all that matters.

If one is foolhardy enough to try and do geometry there, the triangle thought experiment can be taken much further. A correction to the geometry will be needed for both latitude and the rotation of the Earth and its orbit around the Sun and the tidal pull of the moon and the Sun and any mass concentrations in the system, and the Sun's path around the Milky Way, and its inevitable fall into the Andromeda galaxy. That would be chasing the spectre of an absolute space that was supposed to be dead in 1905, wouldn't it? Maybe someone should stop teaching such rubbish and pretend it is anything like a working knowledge of physics or even math. Teach what relativistic Doppler shifts are. Teach it FIRST.

Last edited: Nov 24, 2015
22. ### Farsight

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I'm thinking inflation is a busted flush. And totally superfluous. Now that the Einstein digital papers are online, you can read Einstein saying a gravitational field is a place where the speed of light varies. Then you can find things on the internet saying the "coordinate" sped of light is zero at the black hole event horizon. Then you can find other stuff on the internet wherein the universe is likened to an inside-out time-reversed black hole. The universe expanding over time is like pulling away from a black hole across space. Only your starting position isn't some point-singularity. It's some weird fundamental state of space where the speed of light is zero, and everything's the same. You just don't need inflation to make everything the same. Note though that this doesn't mean big bang cosmology is wrong. We have good evidence that the universe is expanding. But we don't have any evidence for an "inflaton".

23. ### The GodValued Senior Member

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"inflation isn't falsifiable, it's falsified; BICEP did a wonderful service by bringing all the Inflation-ists out of their shell, and giving them a black eye."..........Penrose.