least time

[AntonioLao]

There can be no other principles in physics that is more misunderstood or misstated than the principle of least time. Since this principle was originally discovered by Fermat in 1650 it is often known as Fermat’s principle. The same Fermat who was famous for his last theorem which was really a conjecture until 1996 when Andrew Wiles proved it correct and rightfully promoted it to the true status of a theorem. Now back to Fermat’s principle.

According to Richard Feynman the incorrect statement is the following: out of all possible paths that it might take to get from one point to another, light takes the path which requires the shortest time. Page 26-3, Volume I, the Feynman Lectures on Physics. On Page 26-7, Feynman gave the correct statement as the following: a ray going in a certain particular path has the property that if we make a small change (say a one percent shift) in the ray in any manner whatever, say in the location at which it comes to the mirror, or the shape of the curve, or anything, there will be no first-order change in the time; there will be only a second-order change in the time. In other words, the principle is that light takes a path such that there are many other paths nearby which take almost exactly the same time. More discussions can be found in Feynman’s book QED: The Strange Theory of Light and Matter. He was so convinced; he developed a new version of quantum mechanics using the theory of path integrals. On the other hand, according to Francis A. Jenkins and Harvey E. White, a correct and complete statement of Fermat’s principle is the following: The path taken by a light ray in going from one point to another through any set of media is such as to render its optical path equal, in the first approximation, to other paths closely adjacent to the actual one, Page 7 of their book: Fundamentals of Optics.

The keyword here is ‘optical path’ and in the book by Jenkins and White, it is defined as the refractive index multiplied by the length of the path. However, in this context, it can be defined as the wavelength of a single wave. If this is equal to the Planck length then it represents the highest frequency and consequently the highest energy photon. Moreover, if the rectilinear path is transformed into the curvilinear path then the photon changes its quantum state from pure energy to pure mass and the radiative EM wave becomes standing matter wave creating a particle of ½ integral spin that is the neutrino. This could provide a simple explanation why during a supernova; the neutrinos were detected before the optically visible photons. Somehow the neutrinos took less time from point A to point B since their de Broglie wavelengths were shorter than Planck length equivalent to half the unit length of quantum space-time as square of energy. In other words, instead of surfing the waves of the quantum vacuum fluctuations the neutrinos are tunneling into the space-time continuum of greater curvatures.

[SteveA]

Here's an interesting idea - light may take all pathways but after information is viewed the first time, repetitions are no longer informative (hence slower pathways appear "informationally void").

The novel and unpredictable component was only novel and unpredictable once - the first and shortest pathway that conveyed the information.

We can similarly take any computational medium of any form and map it into an equivalent constant velocity light space medium. If fact even if the medium was altered, this itself could be seen as the photons (as information regarding the alteration was detected and the shortest distance to an unknown determined as the informative pathway ... wow, spherical space filling and lattices etc. )

[AntonioLao]

That would suggest that the universe got blinded and probably bored from looking its own image over and over again. It becomes the blind watchmaker. Consequently a blind watchmaker doesn't care whether the constructed time-piece rotates clockwise or counterclockwise.

[SteveA]

That would suggest that the universe got blinded and probably bored from looking its own image over and over again. It becomes the blind watchmaker. Consequently a blind watchmaker doesn't care whether the constructed time-piece rotates clockwise or counterclockwise.

Or we could similarly say that evolution in physical terms found no benefit to "seeing it all".

[SteveA]

Consider also that depth information is not conveyed via. a photon. A single photon does not directly give information regarding the distance of the source. In fact a photon only selects a specific detector.

If photons do not convey information regarding depth, and a photon is a complete unit of information in an experience (implying a large number of possible detectors for a conscious experience) then multiple representations of an identical state/photon would appear as the same moment in time (AAAA... = A) and also the origin of a detection would be a subjective determination with no reason to consider the photon as having been detected from the nearest unrevealed source.

This would ultimately act similar to a mental space filling around an origin (with a possible subjective/mental bias as to which possible locations in space the photon could have originated from, though that would add complexity and there could be a model that doesn't require this), though a photon could actually be a wave of diverse units of information filtered/masked via. physical perceptions into a single event or moment in time.

[AntonioLao]

Does this rule out superluminal speed? Many agree that energy and informations could not transfer faster than lightspeed.

[SteveA]

Does this rule out superluminal speed? Many agree that energy and informations could not transfer faster than lightspeed.

This is almost by definition though if we're allowed to consider space warped and is not necessarily even a limit - Relativity only states that things have the option of not moving and aging, but two people could take vacations at different locations in the galaxy and come back to meet up for lunch. Of course, in theory, lots of time will have passed for everything else, but we could potentially have humanity spread across the stars and interacting in many ways that would appear to violate the speed of light, despite light speed limits.

But there's more to this - the wavefunction of light is objective - the context in which an individual photon was measured is subjective and not objectively verifiable.

We could consider individual photons to be what are actually experienced though and not the statistically constructed objective wave function.

Now how fast can a single photon travel?

Look at the NIST definition of a second [url]http://physics.nist.gov/cuu/Units/second.html[url]

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.

Now consider that this is a statistical definition and requires a large quantity of energy relative to that of a single photon.

If you want to define motion and are making a relative measurement then you have to define what stays still or is constant (you have to pick your ruler).

I admit I can't see how light speed or in its current form, the speed of information is a limit unless something can be known without learning. That is not a limit in terms of a perceived spacial velocity and Relativity recognizes this.

The limit is really that you can't simultaineously pick to go to someplace unknown and then at the same time define properties about it - it doesn't matter how physically fast the motion getting there is defined to be.

Consider this from a first person perspective instead of the intangible "God's Eye" view of Relativity trying to see things from multiple perspectives.

If an event is experienced and the information is conveyed via. a photon - the individual photon itself does not define a wavelength for light in an objective form (noone can "see" what color someone else sees or what experience someone else has - reality is constructed from first person experiences).

A single photon appears incapable of conveying much information, except if it could have been detected by a network of detectors for which the 1 of n selection provides the equivalent to a photon of a number ranging from 1 to n. (The energy and wavelength of a photon is determined subjectively - this also agrees with Relativity).

So the properties and position of a photon are subjectively determined.

A single photon can already contain a potentially unlimited quantity of information and energy with an unbounded n - for example, it would take an infinite quantity of energy to make a "random" selection of a real number between 0 and 1, though we could bias this statistical window and reduce the average quantity of energy (for example, if we flip a coin and select whether or not to move to the next element of a list of numbers, the average number of coin flips is 2, though it's unbounded how many it may take to reach a number).

Anyway, my point is basically that any quantity of energy/information is possible to be detected in a unit of time (which in many ways is effectively no physical time at all relative to something else) and there need exist no more than a single photon in the universe (though admittedly this single photon would not be the same as an objectively measured collection of photons - what conveyed the information to an observer regarding a collection of photons - a photon itself and not the collection of them that this "photonic experience" triggered an association with.

In other words, how can unconnected or unrelated photons combine into a knowledge or experience regarding a collection of them, unless they already exist in a unified form somehow - something holds the space together outside photons and can't "travel" in a physical sense between point. If photons are seen as the lowest level discrete form of information, then they have no physical limit to their velocity because they convey information regarding the form of space itself and the positions of objects within it. If we can "see" photons, then something else exists beyond photons conveying the information regarding the "seeing" of such photons and it needs to convey information regarding quantities as well - it has to unite all qualities of an experience into a single "word" of information regarding a moment.

Whenever a limit has been assumed regarding the velocity of light through space, it's always been shown false - the only limit that has remained constant is that you can't observe something before it's observed and that's not a limit at all.

The question is really over not simply how two people can leave Earth and go cruise around the galaxy for a while then come back to Earth and exchange their experiences over lunch (that's already possible under Relativity), but how to do it before everyone else on Earth dies (then again, there may be a component of choice involved here).

Notice that looking out at some distant star and believing it to be more than just a point in the sky is an extrapolation beyond experience - if we went there, we'd encounter unknowns along the way as information is filled in. Expecting the star to be as we imagine it now could be rather unrealistic if we're to simultaineously move to see something that was previously unknown - there may be no paradoxes and there may also be no limits. I think the "speed" of information in a physical sense is almost meaningless - the "bandwidth" of information (in a single experienced moment) is something with more tangible characteristics. - of course you need a little mass to do that and adding a little relativistic mass could assist in that.

To show that light speed is really not a limit to physical motion, consider this scenario - we send out a lot of probes into space to catalog everything we can find - everyone rides in one of these close to the speed of light. We then loop back and collect other information on the way back - everyone might spend a year exploring their part of space - we all meet back a "year" later (the universe at this point can go on its merry way) and link up all the information into the "Matrix" and simulate within 99.9999999% accuracy what it would be like to travel around the universe at whim (all using microwatts of energy) - the bandwidth of the human body is in many ways very low.

Of course that 99.999999% accuracy will diverge and someone will have to keep an eye open on things going on "out there", and when things need and update, but ultimately light speed still existed in all this and noone knew what they knew before they knew it and someone actually had to go out there and explore it and we couldn't predetermine what that would be.

[AntonioLao]

What is the physical relation between the photon and the graviton? They are defined with zero rest mass but their energy are not zero. extremely high energy photon has very high frequencies and very short wavelength. The highest energy photon would have wavelength approaching zero which practically rule out its physical existence.

[SteveA]

What is the physical relation between the photon and the graviton? They are defined with zero rest mass but their energy are not zero. extremely high energy photon has very high frequencies and very short wavelength. The highest energy photon would have wavelength approaching zero which practically rule out its physical existence.

The energy of a photon should be determined by its context within a network of mass (memory) relative to the size of the mass.

A graviton need not specifically exist as an attractive force. Photon interactions already imply a connection between emitter and detector hence anything that communicates via. photons could already be considered to have been attracted into an interaction. Attractive or repulsive forces fundamentally just scale space in size and these aren't detectable without inserting or removing components from that space, but if space itself was expanded or contracted (scaled) via. gravity or any other force, this would be unmeasurable.

I'd reply more but I'm going to bed soon.

Let me just show you this real quick so you have a better idea what I'm thinking:

If we have a string of objects in space: ABCD

And we swap two elements ABCD -> ACBD then we can see this as B and C orbiting each other, A attracted to B and C attracted to D as well as B repulsed from B and C repulsed from A.

The reason why I like this linear description is that we can construct 1 to 1 mappings to describe any form of deterministic evolution - you could describe flows of spacial objects in terms of sorting a set of numbers using something as simple as a Bubble Sort http://en.wikipedia.org/wiki/Bubble_sort (though there are more efficient ways of doing it, they aren't necessary and in some ways they might even be physically impractical). A photon under such a model would have two components - a wavelength and a phase, though the size of the set (observational mass) determines the wavelength and so a string of swaps in this sequence could be considered to be a sequence of photon detections within a wavelength or similarly numbers within some range.

Notice that if we randomly swapped elements, it's only a matter of time before every pair of elements is swapped and so statistically, all elements could be considered to attract each other, though this does not require a specific attractive force to do so.

On the other hand, these swaps should not be purely random and so there should exist coherent features in these which could act in quite a few ways similar to resonances within the line segment (notice that if we swept across a segment and swapped adjacent elements, this would cause the segment to rotate like a ring and we could see this composed as two motions - the smaller particle that rotates quickly in one direction and the larger mass that rotates slowly in the other direction - the ratio of these is related to the wavelength of the oscillation).

I apologize for not giving stronger correlations to specific physical particles but I admit it's still not nailed down yet ... the work is still in progress.

(I've to get some sleep for now but hopefully you get a better picture of what I'm thinking - there should be a way to map any physical motion to the equivalent of sorting numbers on a number line and the difference between these two forms is similar to a cause/effect objective view of physical laws constructing the universe versus the subjective selection of events over time - it seems as though it should be theoretically possible, the question is if there's a natural manner in which these two sequences should grow that would simplify how they're interleaved - it could be that each space has restrictions on how the form can grow)

[AntonioLao]

Could this random swap be used to define a physical property called spatial frequency? In contrast to temporal frequency as the reciprocal of a time interval, spatial frequency is the reciprocal of a distance interval.