Tuesday, March 11, 2008

Tipping LightCones and the Escape Velocity of a Photon

"Black Hole" by Tamsin van Essen Also see: Tamsin van Essen-Ceramic Design

Wonderful and creative thinking to what remains a mystery to a lot of people who do not ever get to see what cancer looks like or what it can do to one's family. This physical process, and the creative representation is a very interesting one to me.

Figure 2. Clebsch's Diagonal Surface: Wonderful.
We are told that "mathematics is that study which knows nothing of observation..." I think no statement could have been more opposite to the undoubted facts of the case; that mathematical analysis is constantly invoking the aid of new principles, new ideas and new methods, not capable of being defined by any form of words, but springing direct from the inherent powers and activity of the human mind, and from continually renewed introspection of that inner world of thought of which the phenomena are as varied and require as close attention to discern as those of the outer physical world, ...that it is unceasingly calling forth the faculties of observation and comparison, that one of its principal weapons is induction, that it has frequent recourse to experimental trial and verification, and that it affords a boundless scope for the exercise of the highest efforts of imagination and invention. ...Were it not unbecoming to dilate on one's personal experience, I could tell a story of almost romantic interest about my own latest researches in a field where Geometry, Algebra, and the Theory of Numbers melt in a surprising manner into one another.

It also reminded me of the Wunderkammern and the move to "geometrical design," which was housed in Glass cases and for a time lost to the public eye. Sylvester surfaces is a case in point when looking at the nature of these geometrical models

I am interested in determining how one can detect a blackhole.

So the following post is in latex language that can be copied and those who have latex can place for examination. Clifford's spam checker(just recently checked and see that it was posted.) will not allow me to complete the rest of the comment entry so I will just put it here and go to bed. I tried putting in his latex sandbox(this now worked as well), but to no avail either.

Text book or not, it gives a clearer picture of what a "strong gravitational space" does to the photon.

Gravity and the Photon

The relativistic energy expression attributes a mass to any energetic particle, and for the photon


The gravitational potential energy is then

[tex]\LARGE U=\frac{-GMm}r=\frac{-GMh}{rc^2}{vo}[/tex]

When the photon escapes the gravity field, it will have a different frequency

[tex]\large hv=hv_o[{1-}\frac{GM}{rc^2}] \hspace9 v=v_o[{1-}\frac{GM}{rc^2}] \hspace9 \frac{\bigtriangledown v} {v_o}={-}\frac{GM}{rc^2}[/tex]

Since it is reduced in frequency, this is called the gravitational red shift or the Einstein red shift.

Escape Energy for Photon

If the gravitational potential energy of the photon is exactly equal to the photon energy then

[tex]\normal hv_o=\frac{GM}{rc^2}{v_o} \hspace9 \text or r=\frac {GM}{c^2}\\ \text so if Mass M collapses to radius r a photon will be redshifted to zero frequency[/tex]

Note that this condition is independent of the frequency, and for a given mass M establishes a critical radius. Actually, Schwarzchilds's calculated gravitational radius differs from this result by a factor of 2 and is coincidently equal to the non-relativistic escape velocity expression

[tex]v_e_s_c_a_p_e_ = \sqrt {\frac{2GM}{r}} \hspace9 \\ \text which if V is set equal\\to c gives a radius r=\frac {2GM}{c^2}\hspace9 \text Schwarzchild Radius[\tex]

This equivalence is used as a mnenomic, but does not imply this is a valid way to derive the Schwarzchild Radius

You can delete from your tipping light thread. Have a nice day. I acknowledge fully I am the student. While we see tipping light cones there is an actual qualitative understanding for the determination of the blackhole in this context? By your definition you were right to let me know, how you are presenting this for better consumption and how I might be interfering with that process. So my apology (my bad).

Previously, I left a comment in relation to Susskind's thought experiment about the elephant and Bob on the back of the elephant B moving toward the horizon of the blackhole. My thoughts were about the "entanglement process" and how Alice on the back of elephant A would reveal aspects of the nature of the blackhole as elephant B move closer to that horizon.

This point, while understanding the representation of CFT in this regard, I thought it quite humorous that Susskind did in fact use the elephant as a representative thinking in relation to Quantum gravity? I do not know if people picked up on this?

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