Quote:

---

venetianblinds said:
does hv=mc^2?

---

Quote:

---

venetianblinds said:
E=mc^2


E=hv

is there a relation between these?


does hv=mc^2?

does this even make sense

mc^2=hc/λ  ?

---

Yes, there is a relation between the two.

In general,



Now it only simplifies to when 'p' is zero.  'p' is the momentum.  If we translate our lab into the rest frame of a particle then p is zero and the equation simplifies.  But!, if we are not in the particle's rest frame we must include the 'p' term.

Now consider light.  We have,



Now equate these two equations,



Note that light has no mass!  So instead of the 'p' term dropping out like your original post assumed, it is in fact the 'm' terms that drops out.  This gives us,



Now using a little quantum mechanics and relativity we have the relationship between a photon's energy, momentum and frequency/wavelength.  (Recall that )

Quote:

---

venetianblinds said:
what is the role of planks constant in the uncertainty principle, and how does that relate to the equations above? what does the greater than or equal to mean?

why is energy quantized anyway...

---

Let me respond to the last pondering before the questions.  Asking 'why' can be a tough question to understand.  In 'higher level' sciences why questions are easy, you just appeal to more basic science's theories and say that is why.  But then you run into a problem when you are theorizing about the most basic phenomenon because there is no science that is more basic to answer the why questions with.  The answer to any why question turns out to be the same answer to a what question at a more basic level.  Does that make sense?  ex  Biologist asks, Why does DNA replicate?  Because of chemical bonding and reactions.  Chemist ask, What are the chemical chains doing?  Bonding and reacting.  Why do they bond and react?  Because of quantum mechanics...

That said, we can still muse a bit about why energy is quantized.  Lets think about what prompted the first quantizing of energy by Planck.  He was considering the energy (EM radiation) in a hot container (a black body).  That is, he was considering a glowing hot box where the glowing light inside is bouncing all around back and forth.  He couldn't get the math to jive with the observations.  But he understood the math enough to know that he could 'fix' it by imposing a seemingly arbitrary and adhoc restriction.  Instead of letting the light bounce any possible way he restricted it such that it could only form standing waves with nodes at the box boundaries.  This picture probably looks familiar,



The standing waves must not move at the ends where you can see they are all at zero.  This restricts the kinds of waves you can have.  He applied this restriction to the electromagnetic waves in the hot box (blackbody).  He quantized the energy.

So what about some light/energy that is not in a hot box?  If it doesn't have a wall containing it then its energy modes should not be constrained either.  And that is true.  This situation is known as being a 'free particle'.  A free particle does not interact with any external 'box boundary' (or potential) and thus can have any energy at all, no quantization necessary.  So where can we find free particles?  We cannot.  They are an idealization that does not exist.  Put a particle in the farthest reaches of deep space and it will closely approximate a free particle, but it is still not free because it still feels the electric field, faint as it is, from all the charged particles in galaxies around it.  Does this make sense?  So the more constrained a particle is (the closer the boundaries are to it) the more limited its energy spectrum is.  A less constrained particle has much more energy levels accessible to it.  The limit of this process is for a free particle to have a continuous energy spectrum, but this limit is only approachable and not achievable because forces in the universe have an infinite range.

Quote:

---

what is the role of planks constant in the uncertainty principle, and how does that relate to the equations above? what does the greater than or equal to mean?

---

Planck's constant is just a scaling factor to make our chosen units work out.  Different units entail different values for the constant.  Usually though, when you work with the equations a lot you define your unit system such that h-bar equals 1 exactly (not 1 Js).  This is called using 'natural units'.  (This is done to many of the fundamental constants - speed of light, plancks constant, fundamental electrical charge, boltzmann constant, and others)


becomes,


This convention can be done with the equation in the OP, lets set c = 1 exactly.



becomes,



Now for light mass is zero and we get,



and for a particle at rest we get,

.

Much simpler!  And it works just as good too, as long as you remember the units there are not joules, grams, meters or seconds.

Quote:

---

what does the greater than or equal to mean?

---