High Temperatures

[BlackHole]

We know that there're no physically meaningful temperatures below absolute zero or zero-point energy. At the zero-point energy there is a singularity. It can be shown from the laws of thermodynamics that the temperature can never be exactly absolute zero; this is the same principle that ensures no system may be 100% efficient, although it is possible to achieve temperatures arbitrarily close to it.

 

I was wondering whether the same laws apply to high temperatures. Basically temperatures becomes physically meaningless higher than Planck's temperature at 1.41679 × 10³² K (that's a very high temperature we'll never reach). In fact we have discovered the quark-gluon plasma, a superheated, high-density mass of quarks and gluons which is believed to have existed during the first 20 or 30 microseconds of the Universe's existence.

 

Could there be a singular point much before Planck's temperature?

[Martin]

... Basically temperatures becomes physically meaningless higher than Planck's temperature at 1.41679 × 10³² K (that's a very high temperature we'll never reach). In fact we have discovered the quark-gluon plasma' date=' a superheated, high-density mass of quarks and gluons which is believed to have existed during the first 20 or 30 microseconds of the Universe's existence.

 

Could there be a singular point much before Planck's temperature?[/quote']

 

I never heard of any temperature barrier much before Pl. temp.

As you indicate there are PRACTICAL limitations

 

also various UNPROVEN THEORIES may predict some obstacle to having temperatures higher than some particular scale (like "grand unification scale") which is meaningful in terms of that unproven theory. But I never heard of an generally accepted theory putting a barrier to temperature at some level lower than Planck.

 

Indeed models of early universe tend to have the temperature and energy density at the big bang BE the Planck temperature and energy density.

 

So I say no, the temp that you say is the true temperature max, namely

1.4E32 kelvin

 

(or it could be some order-one factor like 2 times that, or 1/5 that, we should not be too literal, some kind of Planck-scale limit.)

 

But maybe some others will have different ideas

[Martin]

for sure Planck temp is a maximum, or an upper bound, because

at that temperature the thermal radiation (like photons or other jazz) would be so energetic that a quantum of thermal radiation would COLLAPSE ITSELF AND FORM A BLACK HOLE.

 

I think I can even sketch a proof of that if you want.

 

so that would be no fun, you get some thing or some region of space Planckscale hot and it begins to glow and send out light and all the photons immediately are so overloaded with energy that they form small black holes. that has to put a limit on temperature as we understand it

 

BTW the core of the sun, where the fusion is happening, is 15 million kelvin. So how much hotter is Planck temperature?

IIRC Planck temperature is hotter than the core of the sun by about E25,

 

that is by a factor of 10²⁵

 

it gives an idea

[J.C.MacSwell]

This reminds me of a question I've had that is somewhat related, to both this and perhaps the speed of light:

 

Is their a maximum acceleration?

[Martin]

This reminds me of a question I've had that is somewhat related' date=' to both this and perhaps the speed of light:

 

Is their a maximum acceleration?[/quote']

 

In 1976 or so Bill Unruh (British Columbia----a physicist at UBC)

associated a temperature called "Unruh temperature" to any given acceleration

 

if you use natural units, planck units, the Unruh temp is about a/2pi

 

I forget exactly. But the temp is the same order of magnitude as the acceleration when both are expressed in natural units.

 

this means that Planck acceleration (increase speed by c in one Planck time unit) would have Unruh temperature equal to about Planck temp.

 

I think that Planck acceleration is a natural maximum on acceleration because it would be so weird (its Unruh radiation would be forming black holes)

 

So I will propose Planck acceleration to you as a possible universal maximum. IIRC it is about E51 gee. You know what a gee is, of acceleration, the planck accel is roughly E51 times that. I forget exactly.

[J.C.MacSwell]

In 1976 or so Bill Unruh (British Columbia----a physicist at UBC)

associated a temperature called "Unruh temperature" to any given acceleration

 

if you use natural units' date=' planck units, the Unruh temp is about a/2pi

 

I forget exactly. But the temp is the same order of magnitude as the acceleration when both are expressed in natural units.

 

this means that Planck acceleration (increase speed by c in one Planck time unit) would have Unruh temperature equal to about Planck temp.

 

I think that Planck acceleration is a natural maximum on acceleration because it would be so weird (its Unruh radiation would be forming black holes)

 

So I will propose Planck acceleration to you as a possible universal maximum. IIRC it is about E51 gee. You know what a gee is, of acceleration, the planck accel is roughly E51 times that. I forget exactly.[/quote']

 

Couple of thoughts (read "blurt"):

 

If you had a maximum acceleration that would "cap" the high end of frequency for the resulting radiation (an ultraviolet uncatastrophe )...

 

A black body so "capped" would not exhibit the black body radiation "signature"...

 

A black body so "capped" would still exhibit the black body radiation "signature" due to relativity...

 

How does relativity affect temperature?

[BlackHole]

for sure Planck temp is a maximum' date=' or an upper bound, because

at that temperature the thermal radiation (like photons or other jazz) would be so energetic that a quantum of thermal radiation would COLLAPSE ITSELF AND FORM A BLACK HOLE.

 

I think I can even sketch a proof of that if you want.

 

so that would be no fun, you get some thing or some region of space Planckscale hot and it begins to glow and send out light and all the photons immediately are so overloaded with energy that they form small black holes. that has to put a limit on temperature as we understand it

 

BTW the core of the sun, where the fusion is happening, is 15 million kelvin. So how much hotter is Planck temperature?

IIRC Planck temperature is hotter than the core of the sun by about E25,

 

that is by a factor of 10[sup']25[/sup]

 

it gives an idea

 

Thanks Martin. But how did Max Planck arrive at h = 6.626196 x 10^-34 J s? Could it be wrong? How do we know these units are true?

 

Planck's constant has units of energy multiplied by time, but doesn't it speak for itself? Isn't time also energy (because we measure time by seconds)?

 

If Planck's law is true than type III civilizations could be able to get to Planck tempertures, and type IV civilizations must, in order to fit the requirements. We are between Type 0.3 and Type 0.8.

 

Astronomer Don Goldsmith reminds us that the earth receives about one billionth of the suns energy, and that humans utilize about one millionth of that. So we consume about one million billionth of the suns total energy. At present, our entire planetary energy production is about 10 billion billion ergs per second.

 

Planck's temperature implies that the universe will at some point in time run out of energy and collapse under itself to form an enormous black hole. I don't believe this will ever happen.

[swansont]

But how did Max Planck arrive at h = 6.626196 x 10^-34 J s? Could it be wrong? How do we know these units are true?

 

You can measure the maximum kinetic energy of electrons emitted in the photoelectric effect as a function of photon frequency. The slope of the graph is h.

[BlackHole]

You can measure[/url'] the maximum kinetic energy of electrons emitted in the photoelectric effect as a function of photon frequency. The slope of the graph is h.

 

Yes measuring Planck's constant can be done in laboratories provided the right equipment is available. By looking at the blackbody radiation data it's possible to measure Planck's constant. Here's another paper which explains it well.

 

More difficult questions are: Do blackbodies really exist as we think of them? Could the universe be one?

 

I'm sure that future X-ray missions will answer these questions.

[quick silver]

someone said something about absolute zero.......................

 

try looking for a Boise-einstine consendate

they super cooled atoms and sent light throught it.

 

if it's spelled out wrong i'm sorry.