Undergrad Is there a limit to how hot something can get, and if so why?

[a_martin1423]

TL;DR

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Question in the title
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[pinball1970]

Is there an attachment?

 

[pinball1970]

If that is the complete question I am interested in what the limitations are if any. This would be related to what is known about the conditions of the early universe?
Edit: and during collisions in particle accelerators?

 

[Kenneth Watman]

Yes, there is a limit, but some clarification is required. If we heat a substance, say hydrogen and oxygen. we reach a plasma state composed of unbound negative and positive particles moving randomly at high speed and temperture. At that point, can we still say the plasma is composed of water plasma, or is it more accurate to say the plasma is composed of various particles which, if allowed to cool enough, may reconstitute into its original form, water?

I believe the former is the correct answer. When we reach a temperature such that the bonds between the particles constituting water become impossible, I would say we cannot call the resulting plasma water. So the "the limit to how hot something can get" is the temperature at a particular substance becomes a plasma.

There's another way to ask this question. If we can calculate the temperature of absolute zero, can we also calculate the temperature of absolute hot? Is there such a thing as absolute hot? Turns out there is: 1.42 10^32 C aka the Planck Temperature. This results from a calculation based on the Standard Model. Above that temperature and the known laws of physics break down, because matter particles would have to equal or exceed c, the speed of light. Special Relativity suggests such is impossible. For example, the mass of matter moving at c or above is predicted to become infinite. At this point, we have no idea what that could possibly mean.

Obviously we have never reached that temperature on earth. Calculation suggests the closest the universe has come to absolute hot is 10^-42 seconds after the Big Bang or one Planck time. To understand the behavior of matter above that temperature would require a theory of quantum gravity, which, as you know, we don't have. And, if there was no Big Bang, all bets are off.

Just for comparison, the hottest temperature that we have ever actually measured is in the Large Hadron Collider. When they smash gold particles together, for a split second, the temperature reaches 5.5 trillion degrees C. That exceeds the highest measure temperature of a supernova, well short of absolute hot.

https://futurism.com/reddit-depression-mental-illness

 

[PAllen]

It may well be that at Planck temperature known physics is suspect, but there is absolutely no basis to say particles would have to travel faster than c to exceed that temperature. There is no upper bound on kinetic energy, therefore temperature. What is true is that collisions in such a gas would exhibit new physics.

 

[hilbert2]

The object would have to contain enough particles for a thermodynamic temperature to be sensible to define, which sets a lower limit for heat capacity. Then there's a limit for how much energy you can even in principle gather from the surrounding universe to heat that up.

 

[PAllen]

The object would have to contain enough particles for a thermodynamic temperature to be sensible to define, which sets a lower limit for heat capacity. Then there's a limit for how much energy you can even in principle gather from the surrounding universe to heat that up.

That is all true, but irrelevant to the (false) claim that FTL motion would be required to exceed the Planck temperature.

 

[hilbert2]

Sorry, just referring to the title of the discussion.

 

[Kenneth Watman]

Ken Watman back on the line, the first responder to the question whether an absolute hot exists akin to absolute zero. My view remains the same. So far as we can tell based on the latest physics, the limit is the Plank Temperature: 1.42 X 10^42 C, the calculated temperature of the universe one Planck Time after the Big Bang. As the Big Bang remains somewhat controversial, my Absolute Hot answer would need to be changed if the Big Bang theory were to be fundamentally modified or discarded altogether. I love those periods in science.

In reviewing my original answer to this question, I had cause to revisit pleasantly lots of multidisciplinary physics from the Gas Laws to SR to GR to quantum field theory. It was an enjoyable exercise, but I find (within data-supported known or strongly suspected physics) the fundamentals remain simple: K = 1/2mv plus an SR component if you want to nail this question with that much precision. But, in the end, all you really need to know, at the current state-of the-art of physics (replicated ad nauseam) to increasingly long strings of digits, c is a cosmic speed limit on the velocity of information everywhere in the universe and seemingly always has been.

Surprise, we are not the first to consider this question, so I can send whenever is interested a number of good citations. To stay within familiar mathematics, I recommend “https://www.pbs.org/wgbh/nova/zero/hot.html.” It discusses the several answers based in data-supported, current physics that argue in favor of an Absolute Hot limit.

That certainly does not clinch the case. Nothing can in science...in order to be science.

The last possible answer, #5, is that offered by PAllen copied below. The fundamental problem with his critique is that if K=1/2 mv^2 or

It may well be that at Planck temperature known physics is suspect, but there is absolutely no basis to say particles would have to travel faster than c to exceed that temperature. There is no upper bound on kinetic energy, therefore temperature. What is true is that collisions in such a gas would exhibit new physics.

 

[Vanadium 50]

My view remains the same. So far as we can tell based on the latest physics, the limit is the Plank Temperature

That is an urban myth.

As the Big Bang remains somewhat controversial

Not by anyone who knows anything.

 

[PAllen]

...

The last possible answer, #5, is that offered by PAllen copied below. The fundamental problem with his critique is that if K=1/2 mv^2 or

Is it possible your belief in a relation between needing faster than c relative motion to exceed the Planck temperature is based on believing Newtonian kinetic energy is correct except for some 'correction' for SR?

If so, you need to know that this correction is huge. Kinetic energy approaches infinite as speed approaches c, not as speed approaches infinite. Thus, again, no faster than c motion is needed to have arbitrarily high temperature. Specifically, kinetic energy is really mc²( (1/ √ (1 - v²/c²)) -1). For example, at .99999 c, the kinetic energy is over 220 times the energy equivalent of the rest mass of a particle. And, there is just no limit to how high the energy can go without reaching c.

Note, I am not saying anything about various speculative limitations on maximum possible temperature, just that speed being limited to c has absolutely nothing to do with such hypothetical limits.