I've only got a layman understanding of this.
Why did Planck find quantization necessary and how did he come up with the equation E = hf?

I've only got a layman understanding of this.
Why did Planck find quantization necessary and how did he come up with the equation E = hf?
Planck's breakthrough came about in his work to explain blackbody radiation. At the time, available models indicated that the energy radiated from a black body would be infinite due to the contribution from short wavelengths, the "ultraviolet catastrophe". By assusming that radiation occurred in discrete energy packets Planck was able to to produce a model that mirrored what is actually observed.
You can find a more complete discussion in most good physics books. The Feynman Lectures on Physics is particularly recommended.
What amazes me about planck length is how they can assign a value to something which:
a) We can't measure.
b) We don't actually know if it even exists.
and the proceed to construct equations using this value.
1. This thread has absolutely nothing to do with the Planck length.
2. which "exists" as much as does any other defined quantity, and rather clearly has an assigned value.
3. We can't measure a lot of things, for instance , but that does not make them inessential.
4. What is your height to the nearest meters ? Does your height exist ?
Which is fine, but what proof do we have that this is the smallest measurable length?
Or is it just that once you get passed this length, physics no longer makes sense? I always imagined the universe to be "pixelated" and the distance between these pixels would be planck length. I'm not sure if physicists believe that the universe is pixelated or if it's "smooth".
I even see people putting measurements on neutrinos and such, how?! How can they possibly say how small something is when we simply do not have the technology to measure it?
How do physicists come to place figures on things which can not even be measured? I suppose they have weight for a neutrino too?
When I say "people" I mean wiki, google and information available on everyday sites. I've never actually picked up a book from a leader physicist or anything.
http://scaleofuniverse.com/ This is a great interactive tool about the universe, everything from the observable universe down to quantum foam.
Who in the hel said it is the "smallest measurable length ? What is that supposed to mean anyway ?
It sounds like somebody has been reading popsci trash again.
Size in quantum mechanics usually means a crosssection for some sort of interaction. That does have meaning. For a long time it was thought that neutrinos were of zero rest mass. That changed when it was discovered that some types of neutrinos oscillate among types. I think there are some estimates of neutrino mass, but whatever it is, it is very small.
Try doing some actual study, and using reliable sources. Wiki is not a reliable source. Scholarpedia is, but the avvailable topics are limited. Popsci books are generallhy not reliable either, but there are a few that are pretty good  see the thread on popularizations. Better yet see the thread on recommendations for real text books and read some of those. If you have some particular topics in which you are interested ask for references in that latter thread.
There is a lot of crap on the internet.
I wouldn't say that physics no longer makes senses at scales below the Planck length, but rather that it is highly likely that below that point either General Relativity or Quantum Mechanics is going to need revisions in order to be an accurate description of the physical world. What happens at the Planck length is that confining a mass so closely that it is confined to a distance of one Planck length puts enough massenergy within that distance to produce a black hole. But quantum mechanics, which is used to determine how much energy that particle has, assumes that GeneralRelativity effects are negligible. So clearly on length scales close to the Planck length quantum mechanics is going to require some revision. We guess that at the same point General Relativity might need revision as well.
Of course we don't know what those revisions would be, and we will likely need experimental guidance to figure them out. Still, we know quite clearly that something is going to happen to one or the other or both of these two theories.
In the meantime, especially since we are a long way from measuring anything on that small a distance scale, we continue using those two theories in the form we know works very well at the scale we can do experiments. Still, physicists  or at least theorists  would love to see some effects that would give a hint of things to come. The Planck length becomes a target to reach in order to have some fun revising two very fundamental theories.
I think that what you mean is that the existing physical theories do not make sense at such scales. I would agree with that. I suspect that physics itself at that scale will as much sense as quantum mechanics makes at the atomic scale.
Going out on a (very small) limb I would predict that both general relativity and quantum mechanics will require revision in order to arrive at a theory that can address both gravitation and quantum effects. That revision could be radical. I have seen speculation that the model of spacetime as a manifold could break down at such scales, but I have not seen any useful theory based on any other model (yet). Discrete spacetime models have not yielded fruit so far.
String theory appears to have some merit. It has somehow managed to make predictions regarding algebraic geometry that seem to be prescient, in that they have been proved to be true by rigorous methods. It is a excellent conjecture machine. However, it is a long way from being welldefined and has yet to generate any new physical predictions that have any hope of being verified, so I don't know if it represents a viable path to a physical model or is interesting only because of mathematical considerations.
It might help if one could even put existing quantum field theories on a firm mathematical basis. As it now sits neither string theory nor quantum field theories are so grounded, and that makes things rather difficult. The problem may, in part, be that we have not yet developed the necessary mathematics. It would not be the first time that we needed to develop mathematics to reflect needs that were identified in physics  the Heaviside calculus and the Dirac delta leap to mind and required Laurent Schwartz and his development of the theory of distributions to be put on a rigorous basis.
Yes, things become rather opaque when both GR and QM are important.
Do you have any hope that experiment can shed light on things at such a small length/large energy scale in the foreseeable future, or even ever ?
We seem to be having enough trouble at scales that are now achievable with things like lack of evidence for supersymmetry or any extension of the Standard Model.
I don't see much hesitancy in the formulation of theories, even in the absence of experimental guidance. I do see a lack of mathematically welldefined and consistent theories and, most importantly, a complete lack of testable new predictions.
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