'c' in a vacuum? And momentum too?

[Yoron]

"If the photon is not a strictly massless particle, it would not move at the exact speed of light in vacuum, c. Its speed would be lower and depend on its frequency. Relativity would be unaffected by this; the so-called speed of light, c, would then not be the actual speed at which light moves, but a constant of nature which is the maximum speed that any object could theoretically attain in space-time." photon

 

Doesn't relativity build around our ideas of the photon? Feels like building a beautiful construction on a pole, and then say that we don't need the pole as the structure is finished. What am I missing here?

 

And what exactly is momentum of a photon?

'it's relative mass'

But it moves at 'c'?

 

Where does it get this 'relative mass' from?

[Pyrotex]

The photon has energy, which is a function of its frequency.

 

Given E=mc^2, we can turn that around to

 

m = E / c^2

 

This m (mass) is the relative mass (or energy equivalent) mass of the photon.

[Yoron]

Yes, it has a 'energy' that is equivalent to an relative mass mathematically, but how does it 'push'. In much the same manner you can also tell me that a single photon have a frequency, and therefore also is a wave packet. But isn't a photon non classical too?

 

When I try to envision how it 'interact' the nearest I seem to come is that it has an 'impact' but how that impact is transferred I'm still wondering about.

 

And thanks for the answer btw :)

[Pyrotex]

Well HERE is a reference from Wikipedia.

 

Does this help? If not, let me know and we'll keep searching.

[Yoron]

Thanks Pyrotex. I will think some more about it :)

It's not that I don't know, or maybe it's just that that disturbs me, that I don't know.

 

It feels as if I need to start from the beginning with all that I think that I know again to see if I really know anything about it. It's particle/wave-packet duality nowadays confuses me and I'm not sure how to think of it. I will get back to this thread when I feel I have a good question. It seems to be treated as a lot of 'equivalences' with a lot of 'cutoff's'. But I'm not that quick :) so I'll have to think some more. I'll look your link up.

[Pyrotex]

There's one way to avoid the wave/particle duality from bothering you. Pick one or the other. Then confine your discussion to just the properties/attributes of a wave (or of a particle). This almost always works. I don't know of any (simple) problem with photons that require it to be both a wave and a particle at the same time.

 

Here is a better link than the first one. You can click on any of the "bubbles" for detailed discussion. Specifically, click on "photon momentum".

[modest]

Doesn't relativity build around our ideas of the photon? Feels like building a beautiful construction on a pole, and then say that we don't need the pole as the structure is finished. What am I missing here?

 

In relativity c is invariant (that speed is the same in all frames of reference). If light did not travel at the invariant constant c then we would know because the speed of light would not be invariant.

 

~modest

[lawcat]

Yoron, don't worry about it too much. You are not the only one perplexed by the duality.

 

So light, or a photon, is energy ejected from an atom--it is radiation, a wave.

 

Speed of a wave (v) only depends on magnetic permeability (Y), and electric permittivity of a medium (Z). Vacuum, free space, is a baseline medium, with Yo and Zo. In free space, vacuum, the speed of radiation is highest--the speed of light.

 

v^2 = 1 / (Y*Z); or for speed of light in vacuum c^2 = 1/(Yo*Zo) (Constant as modest says aboe)

 

But according to Einstein, there is Energy = mass * c^2. Since radiation has energy and c^2, then it has mass. Then light is also a particle with mass, but because it is radiation then it also is a wave. To reconcile this, we say light has relative mass. (See Freeztar above.)

 

OK. So now, because this makes no sense with radiation having mass, there is a modified Einstein's equation for radiation energy, since radiation has energy, that includes momentum "p," Which depends on wavelength. Energy is the sum of the product of momentum p and speed of light, and the product of mass and speed of light., (E => pc + mc), where mass m = 0. Then, to reconcile this particle which has no mass, which also makes no sense, they call it gluon, which is within the range of other elementary particles called bosons which all have some mass except for gluon. And so the particles grow in the Grand Unified Theory, as well as relationships and equations.

[Yoron]

I'm afraid I'm going to ask a lot of silly questions here :)

 

Okay, do a photon have a size, if not, do it have a dimensionality?

How do we define a dimensionless particle as carrying an energy?

 

And what does that mean if so? If you can have something dimensionless interacting with us, behaving as if it has a velocity inside our SpaceTime, following its geodesics, as well as our arrow of time macroscopically then you have a well defined object it seems? But without interactions, like in deep space unable to observe, right?

 

So we have something that in fact only exist in its interactions, at least it seems so to me. And when it interacts it can do so both as a wave and as a particle, superimposing itself into simultaneous different paths in its mediation with matter, as a wave with several 'real' paths simultaneously as I understands it. As a particle with a probability of those paths, falling out different at each 'real' measurement into only one of those. And depending on definition you can either see it as being 'mediated' by virtual particles or reflected, diffracted, refracted etc.

 

So, how does it move? in a virtual sea of energy (vacuum energy). That would make sense from a particle view, wouldn't it? But from a wave perspective then? Or could it be that as its frame intrinsically is timeless it doesn't have to care for our definitions of distance at all?

 

But then we still need to explain the ocean of light making up our reality, acting inside our arrow of time. Where does its wave behavior come in mathematically, starting as a single photon directly? Or is the idea a superposition even from a single photon perspective mathematically? Also, as I understand it, a photon has no magnetic field (it's zero) and without it, and being timeless intrinsically, how is it thought to create any EM fluctuations (waves) mathematically?

 

And thanks for your answers, I found them all helpful.

(Lawcat, you do have a certain way with words and math:)

 

All thoughts are welcome.

[A23]

I don't know from Maxwell EM, before the Lorentz transform was used, if a photon source can move faster than c, but in the latter case,

 

it's weird that the direction (in dimension 2) of photon can depend on the movement of the observer in relativity, because of a non commutative speed addition, so that we get, when adding orthongal outflying photons to a observer speed v

 

c+v an orthogonal cross centered

 

whereas v+c even if keeping the center fix, has the "arms" bent.

[Pyrotex]

There is another way to understand how photons are created. [deep organ music swells]

 

Forget waves and forget particles.

Think of the atomic nucleus, or an entire atom for that matter, as a cellular automaton .

 

See Wikipedia / Game of Life for an excellent overview of a specific cellular automaton: the famous Conway's Game of Life (CGOL).

 

In the link above, you will see an example of a fascinating CGOL formation that periodically spits out a smaller formation called a "glider". The interesting thing about a glider is that every 4 generations, it reappears, but displaced 1 cell in the X axis and 1 cell in the Y axis. By upping the speed of the generations, the glider appears to move across the game field.

 

As it turns out, this is the maximum speed that any formation in CGOL moves (for an extended duration). It is often called the CGOL "speed of light".

 

In the Wikipedia link, they show a CGOL formation called "Gosper's Glider Gun", which spits out gliders, which travel at the CGOL speed of light. Think of an excited electron around a nucleus as a glider gun. The electron loses its energy by spitting out a photon, which travels at the speed of light.

 

The parallels are quite remarkable. What if at near the Planck Distance, space and time were quantized, and behaved like "cells" in a cellular automaton? What if the "cells" in space-time were either on or off, and the "rules" of how cells turned on or turned off at each quantum of time -- these rules supported the existence of families of "formations" that were essentially permanent.

 

Maybe there are formations for quarks, and three quarks could assemble into a formation for a proton. A much smaller and more primitive formation could make an electron (which might look something like a variable glider gun.) If the electron dropped to a lower orbital, it spit out a "glider" -- a photon! If later, a photon hit the electron, it would absorb the electron and climb to a higher orbital.

 

Now granted, in our universe, photons DO have the property of wavelength. So we have to imagine a cellular automatonic pattern that not only travels at the speed of light (like a glider), but that does so with a variable time length. In other words, the original pattern of a glider repeats every 4 generations. Maybe the original pattern of a photon repeats every P generations, where P is a integer variable.

 

So, now we ask, how does a photon get created? Watch the Gosper's Glider Gun. How does the glider get created? When is it a glider and when is it not, and what is the intermediate form? You may come to the same answer I did. There is no glider, there is no intermediate form, and [poof!] there IS a glider traveling off at CGOL speed of light!!! It isn't--and in the next generation, it IS.

 

If you think this is too farfetched, then read this quote from Wiki:

It is possible to construct logic gates such as AND, OR and NOT using gliders. It is possible to build a pattern that acts like a finite state machine connected to two counters. This has the same computational power as a universal Turing machine, so the Game of Life is theoretically as powerful as any computer with unlimited memory and no time constraints: it is Turing complete.

 

See Conway's Game of Life for a downloadable executable that lets you create your own formations and watch the "game" in action.

[Pyrotex]

And again,

In 1969, however, German computer pioneer Konrad Zuse published his book Calculating Space, proposing that the physical laws of the universe are discrete by nature, and that the entire universe is just the output of a deterministic computation on a giant cellular automaton. This was the first book on what today is called digital physics.

 

In 1983 Stephen Wolfram published the first of a series of papers systematically investigating a very basic but essentially unknown class of cellular automata, which he terms elementary cellular automata (see below). The unexpected complexity of the behavior of these simple rules led Wolfram to suspect that complexity in nature may be due to similar mechanisms.

[Yoron]

That was a totally new one Pyrotex :)

 

I will have to look up your links, but before that. If I consider your analogy, it seems to work in a clockwork SpaceTime? How do you see it encompass f.ex free will. The ability of all biological life to choose and change their minds and movements in SpaceTime? It's more than just complex geometric formations it seems to me?

 

If I should believe what we say we know, everything is light, matter have wave properties too right? So we're down to photons or waves in the end, and there we split it into those following our arrow of time, and those that do not, it seems to me?

===

 

As for meeting a quantized SpaceTime down at a QM level?

 

It's one way of describing it, I too think that there is some sort of transition taking place at Planck level. It seems the logical thing to me :) but when I think of it I think of it in terms of 'emergences', Something begetting new properties and the culprit? If there now is any real culprit, I suspect it to be 'time' which I differ from the 'arrow of time'. But maybe both ideas could work. Mine is a try to define a transition, whereas yours seem to be a way to define the underlying matrix for what might be SpaceTime?

 

Or I could be getting it all wrong. Nevertheless I find our arrow of time being what creates everything we see, if that arrow for example didn't keep a onewaystreet we wouldn't have a causality macroscopically. Then we would need Feynman diagram for macroscopic objects too it seems to me :) Not that I can swear to that but I think most biological systems would stop working in such a universe? At least those complex one building higher biological life. Maybe there are ways for 'life' to exist under such an circumstance but I doubt it would be life that we would be able to communicate with. But who knows :)

 

Interesting idea.

[Yoron]

A23 would you mind expand upon how you think there?

A photon is to me a point particle, having no dimension at all? So why would it matter describing it from a 2D perspective. I'm sure you have a reason for it, so please expand on how you thought so I can see it too.

[A23]

For me in the beginning a photon was corresponding to the vibration of certain modes of the EM field, hence massless, but has some extension in space (in vacuum : a, at c traveling, waveform)

 

Then, I had doubt, classically, since all colors could be made up out of 3 basis colors. If photon were pure waves, this would need an infinite basis of plane waves (Fourier basis for waves), since we can't generate all plane waves from the linear combination of 3 plane waves. So..?

 

For the reality.

 

Now, there are calculation, like the classical electron radius, that do not correspond to reality, but can be made, like :

 

'm_photon' if we suppose p_photon=0, because [math] E^2=m^2c^4+p^2c^2,m_{photon}=\hbar\omega/c^2[/math]

 

then, the 'photon radius' from : [math] r_{photon}=2\frac{G\hbar\omega}{c^4}[/math]

 

 

 

 

 

 

 

Not about the nature of the photon itself, but it's movement, which induced the Minkowski spacetime.

 

Then, If we study a particle able to move in 2 dimension, a plane, found formulas give :

the velocity of particle A seen from obs.1 as relativistic sum of velocity of obs. 2 towards obs. 1 with velocity of part. A seen from obs. 2 :

 

[math]\vec{v}_1:=\vec{v}_2+_n\vec{V}^O_{2vs1}[/math]

 

this operation turns out to be non-commutative. Is this because the observer induces a consciousness ?

 

And hence the question : if we considered 3 observer, and not 2 observer and 1 observed, would we get a commutative operation ? Apparently no since the product of boost isn't.

 

Maybe its the generalizing a priori from dim. 1 that is wrong, and that the adding of a space dimension mathematically changes the properties, even if it seems not intuitive.

[Yoron]

Maybe it's the idea of motion that is questionable here?

we see motion as a function of placement over time and it works well with invariant mass.

But when we come to the Wave Particle duality we find 'sum over paths' as the most correct description.

 

Why?

==

 

and if that is questionable, what does it do to 'distance'?

[Pyrotex]

...Then, I had doubt, classically, since all colors could be made up out of 3 basis colors. If photon were pure waves, this would need an infinite basis of plane waves (Fourier basis for waves), since we can't generate all plane waves from the linear combination of 3 plane waves. So..?...

A23,

most of your post makes no sense at all.

Specifically, your statement above.

"All colors can be made up out of 3 basis colors" applies only to the Human Retina in the eyeball. It does not apply to light or colors in general. It has nothing to do with plane waves, electro-magnetism or physics.

 

The Human Retina contains 4 different light-sensitive cells. One is sensitive to just overall light intensity without respect to color. The other three are sensitive to the specific colors we call Red, Green and Blue. We "experience" a spectrum of colors, because each color in that spectrum (which spans only one optical octave) can be represented by a unique combination of Red, Green and Blue.