"Temperature" can it alter space time

[Naveen_B]

why is temperature not taken as a dimension to study space time ... when the temperature of a particle increases it emitts light or radiations which travel at very high speed .
according to speciel reletivity when an particle moves at speed of light the it actually travells through time ....
we know that different part of univese has different temperature... and energy which is an abstract term has a temperature...
if space can have a temperature then so can time.....



Can any one comment on this.

Regards,
Naveen Balakrishna

[Dickfore]

Clearly you have no idea what temperature is about. It does not make sense to define temperature for anything but a system of a large number of particles. Single particles cannot be attributed temperature.

[Naveen_B]

can you elaborate

[Sakha]

Temperatures is defined as the kinetic energy of a group of particles, always talking in a macroscopic world. You can say what the temperature of a small amount of gas is, but when you go down to the particle world, its nonesense to talk about the temperature of a particle.

[twofish-quant]

why is temperature not taken as a dimension to study space time ...

It is....

http://arxiv.org/abs/gr-qc/9710089

http://arxiv.org/abs/1008.2196

[twofish-quant]

Clearly you have no idea what temperature is about. It does not make sense to define temperature for anything but a system of a large number of particles. Single particles cannot be attributed temperature.

Not true. One thing that Hawking figured out is that black holes must have entropy. Once you have an object with entropy, then you can define a temperature.

What entropy and temperature means in this contact is a pretty active area of theoretical research in quantum gravity.

[twofish-quant]

Temperatures is defined as the kinetic energy of a group of particles, always talking in a macroscopic world.

Temperature is *defined* as what a thermometer measures. (Then you have to define thermometer.)

You can model temperature as how the number of states of a system changes with respect to energy.

You can say what the temperature of a small amount of gas is, but when you go down to the particle world, its nonesense to talk about the temperature of a particle.

Except that you can talk about the temperature of a black hole. If you have a small black hole then it will produce Hawking radiation, and have a well defined temperature, even it looks like a single particle.

It's weird because once you get into the particle world, it's hard to talk about particles. If the temperature of a region of space is high, then particles will spontaneously create themselves.

[Dmitry67]

Whats about temperature and entropy of geometry (of spacetime)?

[Dickfore]

And, I guess black holes are single particles :rolleyes:.

[Sakha]

A question thats pops out for me is that if you heat a sample of gas to really high temperatures, will the RMS velocity reach high speeds in the order of the speed of light (e.g .1c)?

[Dickfore]

It will never overcome it, since the particles will be governed by relativistic dynamics at such high energies. In fact, you will need to use:


E = \gamma \, m \, c^{2}, \; \gamma = (1 - \beta^{2})^{-1/2}, \; \beta = v/c



p = \gamma \, \beta \, m \, c




dp = m \, c \, \left( d\gamma \, \beta + \gamma \, d\beta \right)



d\gamma = \left(-\frac{1}{2}\right) \left (1 - \frac{v^{2}}{c^{2}} \right)^{-\frac{3}{2}} \, \left(-\frac{1}{c^{2}}\right) \, 2 \, v \, dv = \frac{1}{c} \, \beta \, \gamma^{3} \, dv



d\beta = \frac{1}{c} \, dv



dp = m \, \gamma^{3} \, dv \, \left(\beta^{2} + \gamma^{-2}\right) = m \, \gamma^{3} \, dv


Then, the Boltzmann probability distribution (dF = A \, \exp\left(-\frac{E}{k T}\right) \, \frac{d^{3}r \, d^{3}p}{h^{3}}) becomes a speed probability distribution:


f(v) \, dv = A \, \frac{4 \, \pi \, p^{2} \, dp}{h^{3}} \, e^{-\frac{E}{k T}}



f(v) = \frac{4 \, \pi \, A}{c} \, \left(\frac{m c}{h}\right)^{3} \, \gamma^{5} \, \beta^{2} \, e^{-\frac{m c^{2}}{k T} \, \gamma}

[twofish-quant]

Whats about temperature and entropy of geometry (of spacetime)?

People are trying to figure out what that question means.....

http://en.wikipedia.org/wiki/Bekenstein_bound

One thing that it interesting is that a lot of people know Stephen Hawking is a brilliant theorist, but most people can't explain what he did that is so brilliant. It turns out that in the early 1970's, he showed that there are deep relationships between thermodynamics and gravity by coming up with some clever thought experiments about black holes.

The basic idea is this. Suppose black holes really were these giant vacuum cleaners that just sucked in stuff and nothing came out. Then you could make a perpetual motion machine. You throw in your waste heat into your black hole, it disappears, and you can use that to drive a motor that runs forever. Since, we don't think that you can make perpetual motion machines, this must mean that black holes have some temperature so that you can't keep filling up a black hole with your waste heat.

What that means is that there are some fundamental connections between temperature, gravity, and space time, and people have been trying to spend a lot of time since the early-1970's trying to piece together those connections.

[twofish-quant]

A question thats pops out for me is that if you heat a sample of gas to really high temperatures, will the RMS velocity reach high speeds in the order of the speed of light (e.g .1c)?

Yes, and in calculating the behavior of gases at high temperatures, you have to take into account relativity. One thing that happens is that things become floppy, which is why white dwarfs collapse into neutron stars.

[Chronos]

I'm sure twofish did not intend to infer white dwarfs are the progenitors of neutron stars, so, I thought clarification might be helpful. A white dwarf cannot normally acquire enough mass to become a neutron star because, as its mass approaches the Chandrasekhar limit [~1.4 solar mass], it will undergo a runaway fusion process resulting in a type Ia supernova. Neutron stars are believed to originate from core collapse [e.g., type II supernova] of massive [>8 solar] stars.

[Dmitry67]

Holographic principle and Bekenstein bound are interesting, but they are about information/entropy/temperature of matter in spacetime, i was talking about information/entropy/temperature of spacetime itself

Example: empty space with the same boundary conditions (flat at infinity) can be in different states: information can be encoded in the gravitation waves. Gravitation waves carry energy. So you have: information, entropy and temperature in absolutely empty space - even without the matter.

[Chronos]

It is true that gravity waves propogate through empty space, but, they have no definable properties until they interact with matter.

[Dmitry67]

It is true that gravity waves propogate through empty space, but, they have no definable properties until they interact with matter.

Why is it relevant?
You can apply the same logic to wavefunction and measurement devices.