Exploring Heisenberg's Uncertainty Principle & the Big Bang

[Dmitry67]

We can apply Heisenberg's uncertainty principle (between energy and time) to the Big Bang.

In early universe, at moment t, no energies below h/t were possible in principle because there was not enough time for such low energies to manifest. That minimal energy defines a minimal temparature which is about

Thup=Tplank/t (t measured in plank units)

At the same time, actual temparature of the universe descreased as 1/sqrt(t). As actual Temperature decreased slower then Thup, very soon T>Thup and actual particles appeared from the foam.

Is that logic correct?

 

[Chalnoth]

We can apply Heisenberg's uncertainty principle (between energy and time) to the Big Bang.

In early universe, at moment t, no energies below h/t were possible in principle because there was not enough time for such low energies to manifest. That minimal energy defines a minimal temparature which is about

Thup=Tplank/t (t measured in plank units)

At the same time, actual temparature of the universe descreased as 1/sqrt(t). As actual Temperature decreased slower then Thup, very soon T>Thup and actual particles appeared from the foam.

Is that logic correct?

It just makes no sense at all. The temperature of the universe basically has nothing at all to do with the Heisenberg uncertainty principle, which in this case deals with fluctuations in energy not absolute values. Furthermore, the temperature of the universe isn't some simple monatonic thing: it didn't always decrease, and when it does decrease, it doesn't always do so at the same rate. The temperature of the universe depends critically upon the behavior of the matter that makes it up.

 

[BillSaltLake]

Ignoring inflation, at times of about 10^-10 sec & earlier, there were probably only photons and neutrinos. The average energy per particle (photon, neutrino) was proportional to t^-1/2. Massive particles could only exist somewhat later.

If this were extended back to 10^-43 sec, an average photon would have a wavelength comparable to its Schwarzschild radius.

Even including inflation, there would still be a time when this was the case. The physics before that time is of course not yet clear.

 

[Chalnoth]

Even including inflation, there would still be a time when this was the case.

Uh, not necessarily. It's not yet clear what sort of state inflation would have started from, and it's certainly not clear that it either did or even could have started from a state of radiation domination.

 

[marcus]

We can apply Heisenberg's uncertainty principle (between energy and time) to the Big Bang.

In early universe, at moment t, no energies below h/t were possible in principle because there was not enough time for such low energies to manifest. That minimal energy defines a minimal temparature which is about

Thup=Tplank/t (t measured in plank units)

At the same time, actual temparature of the universe descreased as 1/sqrt(t). As actual Temperature decreased slower then Thup, very soon T>Thup and actual particles appeared from the foam.

Is that logic correct?

IMHO this is a rough back-of-envelope calculation. I don't know if it is useful, but the reasoning makes sense to me. I think sometimes a very simple rough calculation like this can reveal something that a more correct but elaborate analysis would miss. So I want to try this out.

If I understand, you are talking about the appearance of matter particles out of a hot vacuum. We do not specify what gives the vacuum an energy density, a temperature, only that something makes it hot. (Something analogous to radiation?)

The key point of the analysis is that for matter to arise, there needs to be BOTH energy and time. The ∆t of the HUP can be no larger than the age t.

By abuse of notation, we think of temperature T(t) as an energy. We put things in Planck units and interpret the HUP as saying t x T(t) > ∆t x ∆E > 1. Therefore we see that:

For matter particles of any sort to come into existence we must have T(t) > 1/t.

But then look! we say. This inequality will happen because the temperature decreases more slowly than 1/t. The temperature decreases as 1/sqrt(t).

Dmitry, is this essentially what you are saying? It seems like a simple observation, and leaves a lot out, but having said that, to me it makes good sense.

 

[Dmitry67]

Marcus, yes. I would just inverse your

"We do not specify what gives the vacuum an energy density, a temperature, only that something makes it hot."

I wanted to say that even in principle, we can not imagine a cold beginning. Because if one claims that the BB was cold (and , say, reheated at very early epoch) the that claim is equivalent to T<{some temperature} at early universe, or Eparticle<{some energy}

But that claim violates HUP. So even purely mathematically, Universe could not start (at Plank time) at any temperature except Tplank. So we don't need to specify where that temperature came from, because we can't imagine the cold universe at the beginning even theoretically

 

[Chalnoth]

Marcus, yes. I would just inverse your

"We do not specify what gives the vacuum an energy density, a temperature, only that something makes it hot."

I wanted to say that even in principle, we can not imagine a cold beginning. Because if one claims that the BB was cold (and , say, reheated at very early epoch) the that claim is equivalent to T<{some temperature} at early universe, or Eparticle<{some energy}

But that claim violates HUP. So even purely mathematically, Universe could not start (at Plank time) at any temperature except Tplank. So we don't need to specify where that temperature came from, because we can't imagine the cold universe at the beginning even theoretically

Yeah, this idea still makes no sense whatsoever to me. The numbers kinda sort of work out just because of dimensional analysis. But your usage of the Heisenberg uncertainty principle just doesn't seem to have anything at all to do with how it's defined.

The energy-time uncertainty principle talks about how long a state will last depending upon its energy. For example, if you look at a high-energy particle in a collider, it will have an uncertainty in its mass that is directly related to its mean lifetime through the energy-time uncertainty principle. Or if you have a system in a superposition of two energy states, then those two states will oscillate between one another in a time given by the energy-time uncertainty principle. Or if you have a vacuum fluctuation that differs from the vacuum energy by some amount, then its lifetime will be given by the energy-time uncertainty principle.

This uncertainty principle, then, doesn't appear to be even remotely related to the subsequent evolution of a newly-formed universe. It does have something to say about how such a universe appears from the outside (as in, a black hole that rapidly evaporates), but not about how it evolves as seen from the inside.

 

[Dmitry67]

For example, if you look at a high-energy particle in a collider, it will have an uncertainty in its mass that is directly related to its mean lifetime through the energy-time uncertainty principle.

Correct. So, if lifetime of a particle is very short, the mass is not well defined.
In early Universe lifetime of ALL particles was very short, hence... masses/energies of all particles were not well defined.

For example, there was no difference between the generations because, for example, electron and muon are similar except their mass, but it early Unvierse there was not enough time for such difference to manifest (I ignore the fact that probably all particles were massles in early universe)

 

[Chalnoth]

Correct. So, if lifetime of a particle is very short, the mass is not well defined.
In early Universe lifetime of ALL particles was very short, hence... masses/energies of all particles were not well defined.

For example, there was no difference between the generations because, for example, electron and muon are similar except their mass, but it early Unvierse there was not enough time for such difference to manifest (I ignore the fact that probably all particles were massles in early universe)

Well, no, not necessarily. The typical particles may well have had lifetimes far in excess of their typical interaction times. In fact, they probably did, given that they were likely all highly relativistic.

 

[Chronos]

HUP limits the maximum possible temperature of the universe, not much more. When photon wavelength reaches the Planck limit - you have the maximum possible temperature. This is commonly referred to as the Planck temperature. It is very hot.

 

[Dmitry67]

HUP limits the maximum possible temperature of the universe, not much more. When photon wavelength reaches the Planck limit - you have the maximum possible temperature. This is commonly referred to as the Planck temperature. It is very hot.

?
It limits the MINIMUM possible temperature.
Particle energy in early universe can not be less then h/t
where t is age of the Universe

 

[Chalnoth]

?
It limits the MINIMUM possible temperature.
Particle energy in early universe can not be less then h/t
where t is age of the Universe

No, because the $$\Delta t$$ in the energy-time uncertainty principle has nothing to do with the age of the universe.

 

[Dmitry67]

No, because the $$\Delta t$$ in the energy-time uncertainty principle has nothing to do with the age of the universe.

Why do you deny the uncerteainty to $$\Delta t$$ between t=0 and t?

 

[Chalnoth]

Why do you deny the uncerteainty to $$\Delta t$$ between t=0 and t?

The main issue here is that you're neither talking about an interval in time, nor about an uncertainty in energy.

 

[Dmitry67]

1. why 0 to t is not an interval?

 

[BillSaltLake]

If M and T are the Planck mass and time, and t was the actual time, then (after the time of inflation) <E_photon>/c² was about M(T/t)^1/2 whereas h/(c²t) was about MT/t. They would have been equal only at t=T (but that was the Planck time, which was before inflation, so the average photon energy expression needs to be modified in a not-yet-well-understood way for inflation).

There might have been a time of equality, but the resulting particles would have been extremely massive "Planckons" or something.

 

[Chalnoth]

1. why 0 to t is not an interval?

Because you're not talking about the interval, you're stating that at a specific time t, the temperature will be a certain value.

 

[SpectraCat]

Because you're not talking about the interval, you're stating that at a specific time t, the temperature will be a certain value.

Well, yes technically, but I think I see what he was getting at. He is taking the time interval describing the universe, and using it to restrict the minimum width of the corresponding energy distribution, according to the "energy-time uncertainty principle" (in quotes because it is not really equivalent to the HUP). Then, since energy is a positive definite quantity, that also necessarily sets a lower bound on the mean value of the energy, which I guess is what he means when he says "temperature". So in that sense, his statement is semantically consistent, since a temperature typically refers to an average value.

Of course, one obvious problem with using this formulation (which has not been raised so far AFAICS) is that it is only valid when $$\Delta$$t refers to a time interval where the quantum state in question persists without perturbation, and this does not seem even remotely reasonable in the early universe following the BB.