rational sphere

Originally posted by FabianFnas
The size of a photon is of no interest. The transparancy of a material is.

A photon can go miles through glass (think fibre optics).
But a photon cannot pass a micron of gold.

I think the OP intended the question as a mathematical one so we are going off at a tangent ... albeit an interesting one.

As far as I am aware the transparency of materiels is due to the atoms (strictly speaking I think its the outer electron shell) absorbing then re-emitting photons. So in one sense nothing is truly transparent and nothing truly opaque (think of very fine gold leaf)

Originally posted by wolfgang59
I think the OP intended the question as a mathematical one so we are going off at a tangent ... albeit an interesting one.

As far as I am aware the transparency of materiels is due to the atoms (strictly speaking I think its the outer electron shell) absorbing then re-emitting photons. So in one sense nothing is truly transparent and nothing truly opaque (think of very fine gold leaf)

I think the size of a photon has something to do with its energy, or wavelength. So enough high energy can penetrate any thickness of any material.

What is a size when thinking of a photon? I don't think a photon has any size, it's a point. However, this point has a radius of wich it has influence. Everything this radius with a magnetic or electrical potential disturbs the photon and the photon disturbes back this 'thing'. If the material (like water), cannot disturb photons, then it's transparant. Or else (like gold) it disturbes, then it's opaque.

Does this make sense? Correct me where I'm wrong.

This mean that if the points of the shwere has any potential, enough to disturb the ray of photons, then the where is opaque. Mathematical points has not, hence it's transparant.

Originally posted by FabianFnas
I think the size of a photon has something to do with its energy, or wavelength. So enough high energy can penetrate any thickness of any material.

What is a size when thinking of a photon? I don't think a photon has any size, it's a point. However, this point has a radius of wich it has influence. Everything this radius with a magnetic or electrical p ...[text shortened]... photons, then the where is opaque. Mathematical points has not, hence it's transparant.

So enough high energy can penetrate any thickness of any material

Not sure you are correct Fabian .. but neither am I. I'm sure a photon cannot go through any particle though. Has to be absorption and emition.

Any physicists out there???????????

Originally posted by FabianFnas
I think the size of a photon has something to do with its energy, or wavelength. So enough high energy can penetrate any thickness of any material.

What is a size when thinking of a photon? I don't think a photon has any size, it's a point. However, this point has a radius of wich it has influence. Everything this radius with a magnetic or electrical p photons, then the where is opaque. Mathematical points has not, hence it's transparant.

What is a photon? Is the minimum amount of energy of an eletromagnetic wave, E=hf where h is the planck constant. The higher the frequency (f), the higher is the minimum energy. You can only have multiple integers of this minimum, never a fraction of it. Therefore eletromagnetic radiation is particularized, discrete, not continuous.
Based on this definition, it does not make sense indeed to think of "size". Photons don't have mass and therefore move at the speed of light (in the vaccuum).
What do you guys think?

Originally posted by Palynka
In topology, dense sets are subspaces of a topological space and so are said to be dense in that space. It's a characteristic of subsets, not spaces. In that sense, the rationals are actually a dense subset of the real numbers!

However, the space generated by a real sphere with a point removed will not be a compact because you can construct a seque ...[text shortened]... of points within that space that in the limit approaches the removed point (outside the space).

@ first bit: Yes, it's why I put the word 'subset' in there. I should have typed it out but I didn't think it would contribute much as people who know topology would probabely know what I mean 🙂

@second bit: The rational sphere with a bigger hole (an open subset missing) is compact. Compact alone doesn't cut it. Though my brain is sluggish today so I might miss something important 🙂

Originally posted by wolfgang59
[b]So enough high energy can penetrate any thickness of any material

Not sure you are correct Fabian .. but neither am I. I'm sure a photon cannot go through any particle though. Has to be absorption and emition.

Any physicists out there???????????[/b]

I'm open to be corrected.

A photon is a particle of light, we usually say, but in reality it's a particle of any electromagnetic radiation, from radio waves to gamma radiation, and beyond. There is no theoretical limit of how much (or less, but a photon without energy is not really a photon, is it?) energy a single photon can have. When the energy is high enough, then there are nothing that can absorb it (exept a black hole, but that's another story). Therefore, with a enough energy a photon can penetrate anything, and everything is therefore transparant for it.

Again, I'm happy to be corrected.

Originally posted by TheMaster37
@second bit: The rational sphere with a bigger hole (an open subset missing) is compact. Compact alone doesn't cut it. Though my brain is sluggish today so I might miss something important 🙂

Ah, I see what you mean. Either way, showing it's not compact should be enough to (dis)prove the original question (well, wolfgang's example was also enough), but I agree that there are compact sets like the one you describe which would allow us to "see through".

Wouldn't local compactness PLUS the definition of sphere be potentially sufficient and necessary conditions, though? Mmm... If not, I don't see how to go about it to be honest...

Either way, I'm not sure how density would help as the rationals are a dense subset of R, yet we know that we can draw a line on the R^3 space which would not intersect any point on the rational sphere.

Originally posted by Palynka
Wouldn't local compactness PLUS the definition of sphere be potentially sufficient and necessary conditions, though? Mmm... If not, I don't see how to go about it to be honest...

i think that you're right that these would be necessary and sufficient - once compactness is proven, i believe it's relatively obvious (if not entirely rigorous) that no point on the surface of the sphere is "special" in comparison to the others. the sphere can be oriented in any arbitrary rotation around the origin and thus any point on the surface treated the same way as any other point on the surface. but then local compactness proves "global" compactness. (?)

if this were a torus or a sphere made out of swiss cheese, i'd beg to differ, but my intuition says this is sufficient.

Originally posted by Aetherael
the sphere can be oriented in any arbitrary rotation around the origin and thus any point on the surface treated the same way as any other point on the surface.

I like that. I was a bit unsure what to do with the definition of the rational sphere in order to use it, but that does it nicely.

Originally posted by Palynka
I like that. I was a bit unsure what to do with the definition of the rational sphere in order to use it, but that does it nicely.

QED!... no seeing out of rational spheres.

Originally posted by Aetherael
QED!... no seeing out of rational spheres.

LOL! Not so fast! It isn't locally compact, so there's seeing out of rational spheres... (if line of sight = line in R^3)

Originally posted by Palynka
LOL! Not so fast! It isn't locally compact, so there's seeing out of rational spheres... (if line of sight = line in R^3)

Originally posted by TheMaster37

I can disprove the existance of any hole of size epsilon (from here on E)

Given an interval (x, x+E) you can always find a rational inside that interval.

Take a rational interval around the given interval. Take the middle of that interval. If that middle is in (x, x+E) you're done.
If not, take the half that contains (x,x+E)

If you continue in this manner you will eventually end up with a point in (x,x+E)

The 3-dimensional variant goes quite similar

whoops! sorry i was thinking that TheMaster's post from the other thread had local compactness... but i'm not a topology guy so i don't really know the difference between "compactness" and "denseness." perhaps i am a dense subset of the real population. 🙂 is there still more work to be done? did i miss a disproving of local compact-itude?

Originally posted by Aetherael
did i miss a disproving of local compact-itude?

To disprove it, all you need is to construct a sequence of numbers within the set that converges to a number outside the set. So if you pick any sequence that converges to say (sqrt(1/3),sqrt(1/3),sqrt(1/3)), then you disprove local compactness. Since the set is dense (using your proof) we know that we can get arbitrarily close to any point on the real sphere so such a sequence exists.

Originally posted by FabianFnas
I'm open to be corrected.

A photon is a particle of light, we usually say, but in reality it's a particle of any electromagnetic radiation, from radio waves to gamma radiation, and beyond. There is no theoretical limit of how much (or less, but a photon without energy is not really a photon, is it?) energy a single photon can have. When the energy is h ...[text shortened]... ything, and everything is therefore transparant for it.

Again, I'm happy to be corrected.

There are no known photons with energy greater than 150 KeV, are there?

Originally posted by smaia
What is a photon? Is the minimum amount of energy of an eletromagnetic wave, E=hf where h is the planck constant. The higher the frequency (f), the higher is the minimum energy. You can only have multiple integers of this minimum, never a fraction of it. Therefore eletromagnetic radiation is particularized, discrete, not continuous.
Based on this definition, ...[text shortened]... ave mass and therefore move at the speed of light (in the vaccuum).
What do you guys think?

But does then a photon have volume? I'm confused 😕