What is the minimum energy limit of particles in the early universe?

[chrisina]

Just a stupid question (?), I have read about Planck time, length, etc... as possible smallest measurable elements of space-time. Is there such a concept for energy ?

 

[marcus]

Just a stupid question (?), I have read about Planck time, length, etc... as possible smallest measurable elements of space-time. Is there such a concept for energy ?

energy and wavelength tend to occur as reciprocals------a high energy particle has a short wavelength. Low energy is associated with slow frequency and long wavelength.

I've not heard anything about a "smallest measurable energy"---which is what you are asking about.
I guess it would be associated with an idea of a longest possible distance, or a lowest possible frequency. (like one cycle takes billions of years :-))

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an extremely small energy would not be part of the Planck system of quantities, in any case.
the Planck energy is around 2 billion joules-----roughly the energy content of a car's tank of gasoline.

many of the Planck units are extreme one way or the other, but not all of them are extremely small. Some of the Planck units are big. Like the Planck unit of speed (one Planck length per Planck unit time) is the speed of light.

Similarly the Planck FREQUENCY for example (where something happens repeatedly every Planck unit of time) is an extremely HIGH frequency.

the Planck temperature is around what cosmologists estimate was the temperature at bigbang time.

the Planck unit of POWER, which delivers one Planckunit energy per Planckunit of time, is a very large rate of energy delivery
it is roughly 10²⁶ times the power output of the sun.
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you asked about a "smallest measurable energy" and I can't answer. All I can say is that it wouldn't be part of the Planck system of quantities, and I never heard of it. I don't see right off how you could define such a thing in practical terms. But maybe someone can.

 

[josh1]

I have read about Planck time, length, etc... as possible smallest measurable elements of space-time. Is there such a concept for energy ?

In a sense yes, but it doesn`t occur as a fundamental constant of nature as the Planck quantities do, but rather as the result of a universe being of finite size: Because lower energy systems have longer wavelengths, no systems are allowed whose energies would correspond to wavelengths that are larger than the universe. This would for example put a lower limit on the energies that can be carried by particles at a given moment.

 

[chrisina]

so, would it make any sense to consider h/T where T is the age of the universe as smallest quanta of energy ? I mean, not of much interest nowadays because T is very large, but in the early moments of the universe, where T is a small multiple of t0 (planck time), does it make sense to consider this as a minimum limit ? Thanks for the answers so far.

 

[marcus]

... does it make sense to consider this as a minimum limit? Thanks for the answers so far.

I don't think it makes sense to consider it as a minimum limit
of particle energies when the universe was a few Plancktimes old.

You could think of it as a typical energy, or as a useful energy scale, though.

If you don't mind, I will substitute hbar for your h. So we are talking about the energy hbar/T
where T is equal to a few Planck units of time.

Well suppose T = t_P = Planck time exactly, just to take a simple case.

then

hbar/T = hbar/t_P = E_P = Planck unit energy

that's rather big to be appropriate as a minimal energy but it is a useful scale for particle energies in the early universe