the Planck temperature scale

[Martin]

Starting another thread Admiral J asked an interesting question

 

"What is the highest(heat) possible temperature?

It's interesting that while the lowest possible temp has a value(absolute zero) even though it has never yet been reached.

 

What about the highest or hottest temp possible. The biggest number I've seen is 100Million degrees C, or are there even higher temps?"

 

this thread got a lot of posts but became involved in personality issues and lost contact with the starting question

 

one way to address questions like this is to think about what is the natural scale of temperature---one that makes the formulas clean and simple. And nowadays there is increasing use of Planck scales (length, energy, time, temperature, mass...) because they impress people as comparatively "natural".

 

Planck actually defined the Planck temperature in 1899 and calculated it in Centigrade (now Celsius) to approximately the temp we use today.

 

And you could say that he "predicted the temperature of the Big Bang" because right at the beginning cosmologists postulate a "Planck era" during which the U had Planck temperature and planck density (one planck mass unit per cubic planck length) etc etc. And particles were whizzing around with essentially their kinetic energies being around the Planck energy unit.

 

So cool, but it is ridiculous to say that max planck predicted the temperature of the big bang because he didnt even think about that, he just calculated the temperature as one of his "natural units"

 

but just like the speed of light is an extreme speed, some of the units he calculated turned out to in some way extreme-----extremely short, extremly brief, extremely hot, extremely dense, extremely powerful in ter ms of wattage, extremely strong in terms of force.

 

they didnt even have the Big Bang back in 1899. He was just trying to think up some units which were more universal and "natural" to his way of thinking than the metric ones and whatever else people had come up with so far.

 

but it did happen the temperature he calculated back then, namely

1.4 x 10³² kelvin

is the temp that cosmologists like to talk about existing right at first and then of course things expanded and cooled and it has never been that hot again.

 

at least they used to. Now there are all these inflation scenarios and it is hard to keep track of the latest Big Bang fashions

 

Furthermore it doesnt matter--we dont know what the BB was like and it was a long time ago. what about Planck temperature NOW.

 

Well it is easy to define and using it, and other "natural unit" scales, makes formulas simple, and practically speaking it works as a Top End of the temp scale with absolute zero being

Bottom End, for the simple reason that nobody talks about any temps higher than Planck----BECAUSE the laws of physics melt at that temperature. If you have a box with atoms in it and heat the box then as you approach that temp the matter comes apart into quarks which collide with each other hard enough to form microscopic black holes and it is a realm of the unknown---when things reach those energies and that temperature it is so abnormal as to be beyond reasonable conjecture.

 

(there is a lively interest in inventing planck-scale physics these days but it has not been done, it is no exageration to say that it is an unknown realm, and I for one think of it as the Planck Temperature being the Melting Point of the Laws of Physics, and leave it at that)

 

Another nice thing about planck temp is it has a simple formula

 

there is this basic formula in physics E = kT

where k is Boltzmann constant that connects temp scale with energy scale.

 

at some T, the kT is the energy that is characteristic of things happening at that temp.------like air molecules kinetic energy is 3/2 kT ------like the jiggling energy of atoms in a crystal of metal is 3 kT----like the thermal glow from a hot thing has a mix of photon energies and a rather typical one is kT.

 

So if you look at all the photons flooding in from the sun, a typical energy for one of them to have is kT, where T is the temp at the surface of the sun.

 

Now Planck defined a natural unit of energy and the Planck temperature is simply that temperature for which kT is one unit of energy

 

in his units, k is equal to one. there is a one-for-one correspondence between temp and energy.

 

and Planck made it so that in his units the hbar constant (that relates frequency and energy) is also one.

so Planck energy is just that amount of energy which correponds to a unit of frequency

 

that is, one over his time unit----not "one per second" but one per Planck time unit.

 

so the formulas are real basic

 

well that's enough for now