@notsosureofit Hypothesis - Revision history

Saucyjack: Removed manual section breaks

2015-07-16T17:32:04Z

Removed manual section breaks

← Older revision		Revision as of 10:32, 16 July 2015
Line 89:		Line 89:
	For constant geometrical dimensions, and constant quality factor and input power, the asymptotic behavior of thrust is inversely proportional to the cube of the frequency and proportional to the square of X.		For constant geometrical dimensions, and constant quality factor and input power, the asymptotic behavior of thrust is inversely proportional to the cube of the frequency and proportional to the square of X.

	~~___________________________________________________________~~		== Appendix 1 ==

	== Appendix 1. ==
	~~Appendix 1.~~

	Proof that scaling dimensions inversely proportional to frequency keeps the thrust invariant:		Proof that scaling dimensions inversely proportional to frequency keeps the thrust invariant:
Line 126:		Line 123:
	If the mode shape is kept invariant, for constant quality factor and input power, the thrust force is invariant, independent of frequency when the diameter and the length of the cavity are both scaled to change inversely proportional to the frequency ratio n.		If the mode shape is kept invariant, for constant quality factor and input power, the thrust force is invariant, independent of frequency when the diameter and the length of the cavity are both scaled to change inversely proportional to the frequency ratio n.

			== Appendix 2 ==
	~~___________________________________________________________~~

	== Appendix 2. ==
	~~Appendix 2.~~

	An interesting expression to examine is <math>\cfrac{fc}{g} </math>		An interesting expression to examine is <math>\cfrac{fc}{g} </math>

Notsosureofit at 15:29, 16 July 2015

2015-07-16T15:29:39Z

← Older revision		Revision as of 08:29, 16 July 2015
Line 2:		Line 2:
	The proposition that dispersion caused by an accelerating frame of reference implied an accelerating frame of reference caused by a dispersive cavity resonator. (to 1st order using massless, perfectly conducting cavity)		The proposition that dispersion caused by an accelerating frame of reference implied an accelerating frame of reference caused by a dispersive cavity resonator. (to 1st order using massless, perfectly conducting cavity)

			== Basic Expression ==
	Starting with the expressions for the frequency of a cylindrical RF cavity [https://en.wikipedia.org/wiki/Microwave_cavity#Cylindrical_cavity]:		Starting with the expressions for the frequency of a cylindrical RF cavity [https://en.wikipedia.org/wiki/Microwave_cavity#Cylindrical_cavity]:
	<!-- f = (c/(2π))((X/R)^2+((p*π)/L)^2)^.5		<!-- f = (c/(2π))((X/R)^2+((p*π)/L)^2)^.5
Line 78:		Line 78:
	where Ds = diameter at small end, Db = diameter at big end and ω = angular frequency.		where Ds = diameter at small end, Db = diameter at big end and ω = angular frequency.

			== Example ==
	Here is an example of the force of each mode vs frequency for m = 0 to 10, n = 1 to 5, p = 1 to 3 from the table referenced above.		Here is an example of the force of each mode vs frequency for m = 0 to 10, n = 1 to 5, p = 1 to 3 from the table referenced above.

Line 90:		Line 91:
	___________________________________________________________		___________________________________________________________

			== Appendix 1. ==
	Appendix 1.		Appendix 1.

Line 128:		Line 129:
	___________________________________________________________		___________________________________________________________

			== Appendix 2. ==
	Appendix 2.		Appendix 2.

Notsosureofit at 01:43, 14 July 2015

2015-07-14T01:43:58Z

← Older revision		Revision as of 18:43, 13 July 2015
Line 57:		Line 57:
	<math>T = \cfrac{h}{2Lf}(\cfrac{c}{2π})^2X^2(\cfrac{1}{Rs^2}-\cfrac{1}{Rb^2})</math>		<math>T = \cfrac{h}{2Lf}(\cfrac{c}{2π})^2X^2(\cfrac{1}{Rs^2}-\cfrac{1}{Rb^2})</math>

	Notice that this is the static thrust per photon in a rest (un-accelerated) frame traveling with the cavity. That is to say, thrust is dependent on the acceleration that the physical cavity experiences and goes to zero at the acceleration g. It ~~is not dependent~~ on the linear velocity. (The case of circular motion is different in that the centrifugal "force" is dependent on angular velocity and will negatively affect the thrust.)		Notice that this is the static thrust per photon in a rest (un-accelerated) frame traveling with the cavity. That is to say, thrust is dependent on the acceleration that the physical cavity experiences and goes to zero at the acceleration g. This is an example of a negative feedback system where the steady state acceleration in the cavity frame of a free cavity will always be less than that calculated from the static force. It has no dependence on the linear velocity. (The case of circular motion is different in that the centrifugal "force" is dependent on angular velocity and will further negatively affect the thrust.)

	If the number of photons is <!-- (P/hf)(Q/2pi*f) -->		If the number of photons is <!-- (P/hf)(Q/2pi*f) -->

Notsosureofit at 01:25, 14 July 2015

2015-07-14T01:25:26Z

← Older revision		Revision as of 18:25, 13 July 2015
Line 56:		Line 56:
	<!-- T = (h/(2Lf))(c/(2π))^2X^2((1/Rs^2)-(1/Rb^2)) -->		<!-- T = (h/(2Lf))(c/(2π))^2X^2((1/Rs^2)-(1/Rb^2)) -->
	<math>T = \cfrac{h}{2Lf}(\cfrac{c}{2π})^2X^2(\cfrac{1}{Rs^2}-\cfrac{1}{Rb^2})</math>		<math>T = \cfrac{h}{2Lf}(\cfrac{c}{2π})^2X^2(\cfrac{1}{Rs^2}-\cfrac{1}{Rb^2})</math>

			Notice that this is the static thrust per photon in a rest (un-accelerated) frame traveling with the cavity. That is to say, thrust is dependent on the acceleration that the physical cavity experiences and goes to zero at the acceleration g. It is not dependent on the linear velocity. (The case of circular motion is different in that the centrifugal "force" is dependent on angular velocity and will negatively affect the thrust.)

	If the number of photons is <!-- (P/hf)(Q/2pi*f) -->		If the number of photons is <!-- (P/hf)(Q/2pi*f) -->

127.0.0.1 at 00:43, 3 June 2015

2015-06-03T00:43:23Z

← Older revision		Revision as of 17:43, 2 June 2015
Line 139:		Line 139:
	The three curves represent p=1, p=2 and p=3, where p is the quantum number in the longitudinal direction, for modes <math>TM_{mnp}</math> and <math>TE_{mnp}</math>.		The three curves represent p=1, p=2 and p=3, where p is the quantum number in the longitudinal direction, for modes <math>TM_{mnp}</math> and <math>TE_{mnp}</math>.

	Notice that for a cylindrical cavity, it takes an infinite number of cycles for the photons in the cavity to reach velocity c (if they were free to do so at the acceleration <math>g</math>). For a cylindrical cavity <math>\Delta f</math> is zero (since the the diameters at both ends are the same, and therefore there is no gradient in that case), which means that the acceleration <math>g</math> is zero. Hence the number of cycles <math>\cfrac{fc}{g}</math> approaches ~~Infinity~~ for a cylindrical cavity.		Notice that for a cylindrical cavity, it takes an infinite number of cycles for the photons in the cavity to reach velocity c (if they were free to do so at the acceleration <math>g</math>). For a cylindrical cavity <math>\Delta f</math> is zero (since the the diameters at both ends are the same, and therefore there is no gradient in that case), which means that the acceleration <math>g</math> is zero. Hence the number of cycles <math>\cfrac{fc}{g}</math> approaches infinity for a cylindrical cavity.



	[[File:00 chart21-2.jpg]]		[[File:00 chart21-2.jpg]]

127.0.0.1 at 00:41, 3 June 2015

2015-06-03T00:41:57Z

← Older revision		Revision as of 17:41, 2 June 2015
Line 139:		Line 139:
	The three curves represent p=1, p=2 and p=3, where p is the quantum number in the longitudinal direction, for modes <math>TM_{mnp}</math> and <math>TE_{mnp}</math>.		The three curves represent p=1, p=2 and p=3, where p is the quantum number in the longitudinal direction, for modes <math>TM_{mnp}</math> and <math>TE_{mnp}</math>.

	Notice that for a cylindrical cavity, it takes an infinite number of cycles for the photons in the cavity to reach velocity c (if they were free to do so at the acceleration <math>g</math>). ~~Because for~~ a cylindrical cavity <math>\Delta f</math> is zero (since the the diameters at both ends are the same, and therefore there is no gradient in that case)~~. Therefore~~ the acceleration <math>g</math> is zero ~~for a cylindrical cavity, and therefore~~ the number of cycles <math>\cfrac{fc}{g}</math> approaches Infinity for a cylindrical cavity.		Notice that for a cylindrical cavity, it takes an infinite number of cycles for the photons in the cavity to reach velocity c (if they were free to do so at the acceleration <math>g</math>). For a cylindrical cavity <math>\Delta f</math> is zero (since the the diameters at both ends are the same, and therefore there is no gradient in that case), which means that the acceleration <math>g</math> is zero. Hence the number of cycles <math>\cfrac{fc}{g}</math> approaches Infinity for a cylindrical cavity.



	[[File:00 chart21-2.jpg]]		[[File:00 chart21-2.jpg]]

127.0.0.1 at 22:32, 2 June 2015

2015-06-02T22:32:00Z

← Older revision		Revision as of 15:32, 2 June 2015
Line 140:		Line 140:

	Notice that for a cylindrical cavity, it takes an infinite number of cycles for the photons in the cavity to reach velocity c (if they were free to do so at the acceleration <math>g</math>). Because for a cylindrical cavity <math>\Delta f</math> is zero (since the the diameters at both ends are the same, and therefore there is no gradient in that case). Therefore the acceleration <math>g</math> is zero for a cylindrical cavity, and therefore the number of cycles <math>\cfrac{fc}{g}</math> approaches Infinity for a cylindrical cavity.		Notice that for a cylindrical cavity, it takes an infinite number of cycles for the photons in the cavity to reach velocity c (if they were free to do so at the acceleration <math>g</math>). Because for a cylindrical cavity <math>\Delta f</math> is zero (since the the diameters at both ends are the same, and therefore there is no gradient in that case). Therefore the acceleration <math>g</math> is zero for a cylindrical cavity, and therefore the number of cycles <math>\cfrac{fc}{g}</math> approaches Infinity for a cylindrical cavity.



	[[File:00 chart21-2.jpg]]		[[File:00 chart21-2.jpg]]

127.0.0.1 at 22:31, 2 June 2015

2015-06-02T22:31:08Z

← Older revision		Revision as of 15:31, 2 June 2015
Line 139:		Line 139:
	The three curves represent p=1, p=2 and p=3, where p is the quantum number in the longitudinal direction, for modes <math>TM_{mnp}</math> and <math>TE_{mnp}</math>.		The three curves represent p=1, p=2 and p=3, where p is the quantum number in the longitudinal direction, for modes <math>TM_{mnp}</math> and <math>TE_{mnp}</math>.

	Notice that for a cylindrical cavity, it takes an infinite number of cycles for the photons in the cavity to reach velocity c (if they were free to do so at the acceleration <math>g</math>). Because for a cylindrical cavity <math>~~delta(~~f)</math> is zero (since the the diameters at both ends are the same, and therefore there is no gradient in that case). Therefore the acceleration <math>g</math> is zero for a cylindrical cavity, and therefore the number of cycles <math>\cfrac{fc}{g}</math> approaches Infinity for a cylindrical cavity.		Notice that for a cylindrical cavity, it takes an infinite number of cycles for the photons in the cavity to reach velocity c (if they were free to do so at the acceleration <math>g</math>). Because for a cylindrical cavity <math>\Delta f</math> is zero (since the the diameters at both ends are the same, and therefore there is no gradient in that case). Therefore the acceleration <math>g</math> is zero for a cylindrical cavity, and therefore the number of cycles <math>\cfrac{fc}{g}</math> approaches Infinity for a cylindrical cavity.

	[[File:00 chart21-2.jpg]]		[[File:00 chart21-2.jpg]]

127.0.0.1 at 22:30, 2 June 2015

2015-06-02T22:30:25Z

← Older revision		Revision as of 15:30, 2 June 2015
Line 139:		Line 139:
	The three curves represent p=1, p=2 and p=3, where p is the quantum number in the longitudinal direction, for modes <math>TM_{mnp}</math> and <math>TE_{mnp}</math>.		The three curves represent p=1, p=2 and p=3, where p is the quantum number in the longitudinal direction, for modes <math>TM_{mnp}</math> and <math>TE_{mnp}</math>.

	Notice that for a cylindrical cavity, it takes an infinite number of cycles for the photons in the cavity to reach velocity c (if they were free to do so at the acceleration g). Because for a cylindrical cavity delta f is zero (since the the diameters at both ends are the same, and therefore there is no gradient in that case). Therefore the acceleration g is zero for a cylindrical cavity, and therefore the number of cycles fc/g approaches Infinity for a cylindrical cavity.		Notice that for a cylindrical cavity, it takes an infinite number of cycles for the photons in the cavity to reach velocity c (if they were free to do so at the acceleration <math>g</math>). Because for a cylindrical cavity <math>delta(f)</math> is zero (since the the diameters at both ends are the same, and therefore there is no gradient in that case). Therefore the acceleration <math>g</math> is zero for a cylindrical cavity, and therefore the number of cycles <math>\cfrac{fc}{g}</math> approaches Infinity for a cylindrical cavity.

	[[File:00 chart21-2.jpg]]		[[File:00 chart21-2.jpg]]

127.0.0.1 at 22:27, 2 June 2015

2015-06-02T22:27:32Z

← Older revision		Revision as of 15:27, 2 June 2015
Line 138:		Line 138:

	The three curves represent p=1, p=2 and p=3, where p is the quantum number in the longitudinal direction, for modes <math>TM_{mnp}</math> and <math>TE_{mnp}</math>.		The three curves represent p=1, p=2 and p=3, where p is the quantum number in the longitudinal direction, for modes <math>TM_{mnp}</math> and <math>TE_{mnp}</math>.

			Notice that for a cylindrical cavity, it takes an infinite number of cycles for the photons in the cavity to reach velocity c (if they were free to do so at the acceleration g). Because for a cylindrical cavity delta f is zero (since the the diameters at both ends are the same, and therefore there is no gradient in that case). Therefore the acceleration g is zero for a cylindrical cavity, and therefore the number of cycles fc/g approaches Infinity for a cylindrical cavity.

	[[File:00 chart21-2.jpg]]		[[File:00 chart21-2.jpg]]