Can the Energy of a Photon be Expressed in h/s?

[bobie]

it's not forbidden as far as I know. But it seems that people like to keep 'units' as a separate concept from 'quantities', although I don't see any fundamental difference.
... it is sometimes called 'nondimensionalization'

That is very comforting , so you wouldn't spank me for h/s?

...it says that this is the frequency of a photon with the same energy (via the famouse E=mc^2 relation) as
... in my area we tend to use Hz etc..

That is just what I said in post #9

.. how can we express that the scalar of the frequency is always equal to the scalar of the energy of a photon?

I found this habit everywhere, even in Encyclopaedia Britannica, which is my guidebook, as I can't afford buying texts. After all, dimensions is just a convention. Probably we can say that also scientists use poetic licenses.

 

[f95toli]

After all, dimensions is just a convention. Probably we can say that also scientists use poetic licenses.

Not quite. Everything will ultimatly refers back the SI, which by design is a consistent system of units. The SI is also what use when we realize the units, "realize" in this context means the experimental implementation used for the definitions, e.g. the atomic clocks that are used to realize the second.
While people use a bunch of other conventions, this is just because we are all a bit lazy and want to simplify equations etc. Moreover, everyone who uses these other conventions (e.g. expressing mass in MeV) knows how to convert back the SI (and frequently do so when there is a need).

Hence, if you are a beginner it is generally best to stick the SI, simply because there is less room for confusion.

Note also that it is currently strickly speaking impossible to express mass in eV or Hz (or whatever else you want) if you want an exact result. The reason is that we do not have an exact values for h or e; meaning any conversion is approximate. This is only of academic interest to most people, but is sometimes important in high-precision metrology.

 

[bobie]

I 'll follow in your steps , I'll stick to Hz, no poetic licenses

 

[BruceW]

you mean joules? joules is the SI unit of energy.

 

[BruceW]

Also, about the non-dimensionalized units, it does make sense really, there's no poetic license being used. As long as the person says what kind of system of units they are using, you'll be fine. It is only if they don't say how they have defined things, this could cause problems. For example, they could use $c=1$ or $v_{sound}=1$ where $v_{sound}$ is the speed of sound in air. The first convention means speed will be a dimensionless number as a fraction of the speed of light, and the second convention means speed will be a dimensionless number that is called the Mach number. So if they give you an equation for some velocity $V$ like $V=0.45$ without telling you which convention they are using, this could either mean the velocity is 0.45 times the speed of light, or the velocity is 0.45 times the speed of sound. (or some other convention - you don't know until they tell you what convention they have used).

edit: actually that's not quite right, because Mach number uses the local speed of sound. But you can imagine some 'standard' speed, i.e. speed of sound in still air, at a certain temperature and pressure, with a certain composition.

 

[bobie]

what is confusing, specifically? Or is it just surprising that angular momentum has the same dimensions as energy x time ?

I think dimensions have a sense if they are the fingrprint, DNA of an entity, if the relation is not biunivocal seems more like red tape, a burden; if J.s is the DNA of unrelated conceps like action and momentum I find it confusing. But surely it is my fault.

As to the action, unless someone enlightens me, I cannot imagine to what it corresponds in reality.
I see the sense of *s if an entity has been divided by s to restore its meaning : v = S/T *T = space, distance travelled, P = E/ T * T = E. Likewise, I would be muddled by S*T , what does it mean?
where do you use action, apart from h? that would help me understand!

 

[Dale]

I think dimensions have a sense if they are the fingrprint, DNA of an entity, if the relation is not biunivocal seems more like red tape, a burden

The relation is most definitely not biunivocal. I don't know why you would expect it to be. It isn't even univocal.

 

[BruceW]

Action is a different concept. The time integral of the Lagrangian of the system is the action. But again, action has the same dimensions as energy x time and angular momentum.

Also, J.s is not the S.I. units for momentum. The S.I. units for momentum are J.s/m, or more simply: kg.m/s

 

[Dale]

As to the action, unless someone enlightens me, I cannot imagine to what it corresponds in reality.
...where do you use action, apart from h?

Action is used extensively in Lagrangian mechanics (e.g. the principle of least action):
https://en.wikipedia.org/wiki/Lagrangian_mechanics

 

[bobie]

Physical constants that are not dimensionless:
h: Planck's constant
c: speed of light in vacuum

If c is not dimensionless, how come α is considered dimensionless although it is just 0.00729 c?

 

[Bandersnatch]

although it is just 0.00729 c?

It most definitely isn't. http://en.wikipedia.org/wiki/Fine-structure_constant#Definition
Where did you get that idea from?

 

[bobie]

It most definitely isn't. http://en.wikipedia.org/wiki/Fine-structure_constant#Definition Where did you get that idea from?

From your link:

The ratio of the velocity of the electron in the Bohr model of the atom to the speed of light. Hence the square of α is the ratio between the Hartree energy (27.2 eV = twice the Rydberg energy) and the electron rest mass (511 keV)

.

 

[f95toli]

I don't think you've read that carefully enough.
The ratio two velocities has no dimension, i.e. alpha is dimensionless

 

[bobie]

Isn't 0.1 * 300,000c/s equal to 30,000 c/s?

 

[f95toli]

Isn't 0.1 * 300,000c/s equal to 30,000 c/s?

So?

The link says thatthe ratio of the velocity of the electron in the Bohr model of the atom to the speed of light

The velocity of the electron will have the dimension m/s
The speed of light has the dimension m/s

So if you divide one by the other you get a dimensionless number.

 

[bobie]

The relation is most definitely not biunivocal. I don't know why you would expect it to be. It isn't even univocal.

The point is that people tend to forget that. I think that Dimensions have their own identity like jars and boxes, but can also be , exactly like them, anonymous empty vessels: if you fill them with chocolates then
box*choc and jar*choc
is just the same (choc) and not two different entities, Is that right, Dalespam?, L² is a scalar or an area?
In the other (G) thread (you know) I was frozen by posters who told me that "v²/ r is acceleration": everybody takes L/S² as a fingerprint, nobody said" it might be acceleration, it is also acceleration" and I could not question that, starting an inappropriate discussion. It might be also something else, do you agree?

 

[BruceW]

In the other (G) thread (you know) I was frozen by posters who told me that "v²/ r is acceleration": everybody takes L/S² as a fingerprint, nobody said" it might be acceleration, it is also acceleration" and I could not question that, starting an inappropriate discussion. It might be also something else, do you agree?

yeah, v²/ r could represent some other concept or quantity than acceleration. The thing you can say for sure, is that quantity has the same dimensions as acceleration.

 

[bobie]

The speed of light has the dimension m/s.

Is every speed a fraction of C, since m= C*s/ 3*10⁸?
10 m/s = 10 C*s/3*10⁸*s

 

[Dale]

In the other (G) thread (you know) I was frozen by posters who told me that "v²/ r is acceleration": everybody takes L/S² as a fingerprint, nobody said" it might be acceleration, it is also acceleration" and I could not question that, starting an inappropriate discussion. It might be also something else, do you agree?

No, in the context of the referenced discussion, v²/r was definitely acceleration (no "might" or "maybe"), specifically, it is the magnitude of the centripetal acceleration of a body in uniform circular orbit of speed v and radius r.

However, the dimensions of acceleration depends on the system of units you are using. If you are using SI (or indeed most systems of units) then acceleration has dimensions of L/T². In these units v has dimensions of L/T and r has dimensions of L, so v²/r has dimensions of (L/T)²/L -> L/T².

But if you are using geometrized units then acceleration has dimensions of 1/L. In these units v is dimensionless and r has dimensions of L, so v²/r has dimensions of (1)²/L -> 1/L. But in the absence of clarification of the system of units being used, generally SI is assumed.