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On a TV program with some well-known astrophysicists they sad that the effect of Heisenberg's uncertainty principle shortly after the Big-Bang made matter (normal & dark) expand in a non-homogeneous way.

Now, here's my question: if I understand it correctly, Heisenberg's principle does state that we cannot know - at the same time - the position and momentum of a particle; this due to the wave-like nature of fundamental particles.

What is then the connection between us not being able to know both quantities at the same time and the early universe expanding in a non-homogeneous way? (i.e. forming agglomerations of matter that would become the seeds of stars and galaxies).

Any ideas what these experts were talking about?

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    $\begingroup$ "if I understand it correctly, Heisenberg's principle does state that we cannot know - at the same time - the position and momentum of a particle". No, this is not exactly correct. The HUP states that a particle does not have - at the same time - the exact position and momentum or a specific energy at a specific moment or any pair of parameters that are Fourier conjugates. $\endgroup$ – safesphere Jul 2 '18 at 12:28
  • $\begingroup$ I'm not sure how it relates to the Uncertainty Principle directly, but one of the theories of the origin of inflation is the Inflaton field. Ripples in the inflaton field may have caused the anisotropies we see in the CMBR $\endgroup$ – Beta Decay Jul 2 '18 at 14:44
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    $\begingroup$ This is in reference to the energy-time uncertainty relation, which is interpreted as permitting the existence of quantum vacuum fluctuations: momentary energetic excitations about the vacuum. During inflation, these vacuum fluctuations undergo exponential expansion, and are rendered permanent by this rapid expansion. Quantum fluctuations become classical perturbations, making the universe slightly inhomogeneous. The inhomogeneities were the seeds of galaxies and galaxy clusters, and can be studied by measuring the temperature anisotropies of the CMB. $\endgroup$ – bapowell Jul 2 '18 at 16:24
  • $\begingroup$ @Safesphere: that's a good explanation, it's not about us not knowing... it's about the particle not having an exact position and momentum. I'll have to go back and get the dust off my books about solid state physics (part of a course in semiconductor theory). Thanks! $\endgroup$ – kxtronic Jul 5 '18 at 20:57
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A Quantum fluctuation is the temporary change in the amount of energy at a point in space.

This is part of the Heisenberg uncertainty principle.

This allows the creation of particle-antiparticle pairs of virtual particles.

Quantum fluctuations were very important in the early stages of the universe, according to the model of expansive inflation, the ones that existed when inflation began, were amplified and formed the seed of the current observable universe.

In the early stages of the universe, tiny fluctuations within the university's density led to concentrations of dark matter gradually forming. Ordinary matter attracted to these by gravity, formed large gas clouds and eventually stars and galaxies and voids.

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they said that the effect of Heisenberg's uncertainty principle shortly after the Big-Bang made matter (normal & dark) expand in a non-homogeneous way.

Quantum fluctuation of the early universe are introduced in the Big Bang model because of the great homogeneity observed in the cosmic microwave background, of order $10^{-5}$ , no matter at what part of the observable universe one maps the CMB. It was necessary because at the time of decoupling of light/photons from matter, there were parts of the universe which due to special relativity could not exchange energy with other parts and come into a thermodynamic equilibrium that could explain the perfect black body radiation shape, no matter what part one looked at.

The statement you are quoting is the one hand waved to explain the tiny $10^{-5}$ inhomegenuities that are observed, emphasized in the plots for clarity :

enter image description here

Since the model is quantum mechanical, quantum fluctuations will exist by construction of the theory. The Heisenberg Uncertainty is a rule of thumb for the way the quantum mechanical operators commute or not with each other, and in the CMB map are reflected in the detection of more (or less) radiation over the background, (again , at a level differing from uniform by orders of $10^{-5}$). These bumps are the seeds for the clusters of galaxies and galaxies as the universe expanded after the photon decoupling.

What is then the connection between us not being able to know both quantities at the same time and the early universe expanding in a non-homogeneous way?

The position and momentum uncertainty is one of the possible fluctuations, as there are a number of non commuting operators in the quantum mechanical models, to introduce uncertainty in the behavior of the primordial energy density . It is not necessary that a human observer observes , it is enough that interactions are happening , these are the "observers" , and a lot of interactions of the inflaton are happening in the Big Bang Model.

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This is in reference to the energy-time uncertainty relation, $\Delta E \Delta t \geq \hbar/2$, which is interpreted as permitting the existence of quantum vacuum fluctuations: momentary energetic excitations about the vacuum. During inflation, these vacuum fluctuations undergo exponential expansion, and are rendered permanent by this rapid expansion. Very naively, one can think of the vacuum fluctuation as the creation of a particle/antiparticle pair. In static space, this pair quickly annihilates in a time $\Delta t$ afforded by the uncertainty principle. But, when the space is inflating, the pair is swept apart. Here's a cartoon of this process:

enter image description here

But, one should be cautious about taking this picture, and even an explanation in terms of the uncertainty principle, too seriously. It's most appropriate to study how fluctuations evolve according to quantum field theory in curved space, while avoiding the urge to pin a physical interpretation in terms of particles to the process. These fluctuations generally evolve as plane waves in static spaces, $\delta \phi_k \sim e^{ikx}$. But during inflation, $k \sim a$, and the wavelength grows along with the expansion. When the wavelength of a fluctuation grows to surpass the Hubble scale, which encloses causally-related points in space, the quantum fluctuation becomes a classical perturbation, making the universe slightly inhomogeneous. The inhomogeneities were the seeds of galaxies and galaxy clusters, and can be studied by measuring the temperature anisotropies of the CMB.

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