During inflation how did spacetime 'push' particles

[Quantum321]

It seems to me that Guths inflation of spacetime would just push past the particles? I know all waves possess momentum so were waves effecting the particles?

 

Hmm. Perhaps there were no particles at that time and only the building blocks of quarks? The inflationary epoch lasted 10⁻³⁶ seconds.

I guess I am really asking what stuff existed during that time?

Edited November 24, 2016 by Quantum321

[Mordred]

at that time photons, quark/gluon plasma.

 

Inflation doesn't particularly push particles its rather a rapid expansion of volume due to a phase change. Which closely ties to electroweak symmetry breaking.

 

Do you understand the quantum tunneling aspects behind Guth's false vacuum?

[Strange]

Note that there was nowhere for inflation to push particles "to", as all of space was homogeneously full of whatever particles existed at the time. It was just that the volume of space expanded very rapidly.

[Quantum321]

"Inflation doesn't particularly push particles its rather a rapid expansion of volume due to a phase change. Which closely ties to electroweak symmetry breaking.

Do you understand the quantum tunneling aspects behind Guth's false vacuum?"

 

I get the impression that science is just guessing here.

 

"volume of space expanded very rapidly." I was looking for an answer that was more specific. What is the volume of space and whats inside?

[Strange]

"volume of space expanded very rapidly." I was looking for an answer that was more specific. What is the volume of space and whats inside?

 

 

The volume of space may have been infinite (if the universe is infinite) or quite small, if the universe is finite. What's inside would have been the quark-gluon plasma that Mordred mentioned.

 

But this is near or at the limits of where our current theories of physics can be applied. So you may not get anything much more specific. The whole idea of inflation (and the mechanism behind it) is still very hypothetical and speculative. We probably need a quantum theory of gravity to tell us more.

[Quantum321]

Since I can't conceive of an infinite BB the universe must be finite. All the particles that were created were based on the temperature of the universe at any given time supports BB. Guths 'guess' about inflationary seems to make predictions that are true. The CMR supports the BB. However, is no center of the universe or we just don't understand how to determine it now. So Strange is correct. There is no model that supports what we see. This means there are fundamental problems with our understanding of how the universe began. How can this be? What are we missing?

 

I’ll do algebra, I’ll do statistics, I’ll even do trigonometry…

But graphing, THAT is where I draw the line!

Edited November 24, 2016 by Quantum321

[Delta1212]

Since I can't conceive of an infinite BB the universe must be finite.

 

Your conclusion does not follow from your premise.

[Quantum321]

Your conclusion does not follow from your premise.

Please explain.

[Strange]

Since I can't conceive of an infinite BB the universe must be finite.

 

 

Really? The universe has to match what you, a random individual on Earth, can imagine? Is this written in Genesis or Newtons laws? And why you? I am famously unimaginative; I'm sure I can imagine a lot less than you. So why is the universe limited to what you can imagine and not just what I can imagine?

 

One the other hand, why shouldn't the universe be defined by what Leonardo da Vinci could imagine? Does the universe change with every generation as people with more less imagination are born and die?

 

That is the stupidest statement I have read for a long time.

 

(The rest of your post is just incomprehensible.)

[J.C.MacSwell]

Since I can't conceive of an infinite BB the universe must be finite. All the particles that were created were based on the temperature of the universe at any given time supports BB. Guths 'guess' about inflationary seems to make predictions that are true. The CMR supports the BB. However, is no center of the universe or we just don't understand how to determine it now. So Strange is correct. There is no model that supports what we see. This means there are fundamental problems with our understanding of how the universe began. How can this be? What are we missing?

 

I’ll do algebra, I’ll do statistics, I’ll even do trigonometry…

 

But graphing, THAT is where I draw the line!

I can't either...but my conclusion was a little different...I concluded my brain must be finite...

[Airbrush]

It seems to me that Guths inflation of spacetime would just push past the particles?

 

Why push? If beyond the big bang is a perfect vacuum, wouldn't that vacuum suck the universe apart as inflation?

[Strange]

 

Why push? If beyond the big bang is a perfect vacuum, wouldn't that vacuum suck the universe apart as inflation?

 

 

There is no "beyond". The universe is, and always has been, uniformly full of matter.

[Quantum321]

'Since I can't conceive of an infinite BB the universe must be finite.'

 

Strange your comments to my statement are obvious. I should have elaborated. I am using the standard model of the Big Bang, you know the theory that's in all the text books? Where the entity of the Universe was compressed into a singularity called space-time singularity. This singularity is a location where the quantities that are used to measure the gravitational field become infinite in a way that does not depend on the co-ordinate system.

The creation process of the Universe began with an expansion. The General Theory of Relativity yields an infinite density and temperature at a finite time in the past. This singularity is of which I speak. How can there be an infinite singularity? Now if you want to talk about another theory that has passed peer review please tell me where I can find it.

Its true current theory predicts nothing exists outside the singularity. To me in the very beginning this was a finite point. I can't understand how this can be an infinite point. You say that all future particles exist within this singularity I agree. However, after inflation there must be space-time between which expands the particles. This is my question. I can understand space-time expanding but how could this expanding space-time carry the particles with it?

Edited November 25, 2016 by Quantum321

[Strange]

The General Theory of Relativity yields an infinite density and temperature at a finite time in the past. This singularity is of which I speak. How can there be an infinite singularity?

 

 

No one things it is sensible to extrapolate back to an infinite density. Our current theories no longer apply before you get to that point. Maybe a theory of quantum gravity will tell us what happened. Or maybe we can never know.

 

 

 

This is my question. I can understand space-time expanding but how could this expanding space-time carry the particles with it?

 

A gas will diffuse to fill the space available. And will cool as it does so.

[Quantum321]

 

 

No one things it is sensible to extrapolate back to an infinite density. Our current theories no longer apply before you get to that point. Maybe a theory of quantum gravity will tell us what happened. Or maybe we can never know.

 

 

A gas will diffuse to fill the space available. And will cool as it does so.

Spacetime expanded faster than the speed of light. However, particles can not. Not sure I understand this mechanism in the context of the early universe. Tomorrow is another day.

[Strange]

Spacetime expanded faster than the speed of light. However, particles can not. Not sure I understand this mechanism in the context of the early universe. Tomorrow is another day.

 

 

They didn't need to go anywhere. If they all stayed in the same position in space, they would move apart as the space expanded. The same way the we can see distant galaxies that are receding faster than the speed of light. They are not moving through space faster than the speed of light, so there is no problem.

[Quantum321]

 

 

No one things it is sensible to extrapolate back to an infinite density. Our current theories no longer apply before you get to that point. Maybe a theory of quantum gravity will tell us what happened. Or maybe we can never know.

 

 

A gas will diffuse to fill the space available. And will cool as it does so.

 

However, Einsteins theory predicts infinity density at the singularity. Sounds like we're saying Einstein was wrong.

 

 

 

 

They didn't need to go anywhere. If they all stayed in the same position in space, they would move apart as the space expanded. The same way the we can see distant galaxies that are receding faster than the speed of light. They are not moving through space faster than the speed of light, so there is no problem.

 

I have a problem understanding this. Let's look at Oxygen. I chose this molecule because it is about the same density as air. If I have a canister of Oxygen gas and release it into an auditorium the Oxygen molecules move apart to occupy the new larger space. In this scenario the component molecules of air move in between the Oxygen molecules. This dilutes the Oxygen gas.

At the Big Bang all the particles occupy a given space at a particular time. During inflation spacetime expands faster than the speed of light and must move around the particles because particles can travel the speed of light. This is my point there is no friction from spacetime to move the particles. They should not move.

[Mordred]

Scientists already know GR isn't complete as it cannot directly handle singularity issues

[Quantum321]

Scientists already know GR isn't complete as it cannot directly handle singularity issues

 

Hello Mordred, I guess you're right. He also said the warping of space-time was gravity. Its only one term in the equation of gravity. It's a small factor.

[Mordred]

I have a problem understanding this. Let's look at Oxygen. I chose this molecule because it is about the same density as air. If I have a canister of Oxygen gas and release it into an auditorium the Oxygen molecules move apart to occupy the new larger space. In this scenario the component molecules of air move in between the Oxygen molecules. This dilutes the Oxygen gas.

At the Big Bang all the particles occupy a given space at a particular time. During inflation spacetime expands faster than the speed of light and must move around the particles because particles can travel the speed of light. This is my point there is no friction from spacetime to move the particles. They should not move.

Very good but not quite accurate.

 

A homogeneous and isotropic fluid has equal pressure on every point on an object. So as the volume changes this relationship still holds on expansion.

 

The object gains no inertia as the sum of force in any direction equals zero. This however doesn't prevent the volume from changing between two objects.

 

The objects themself do not move but the distance between them change due to volume change.

Correlating this back to pressure we can accurately express that expansion is not due to pressure as their is no pressure gradient to cause a flow. However pressure can still perform the work for expansion.

 

This is where it differs in your room example. In the case of expansion it modelled as an adiabatic solution. (no net inflow or outflow).

 

This is also why superluminal expansion does not violate GR. As it is not an inertial change.

Edited November 25, 2016 by Mordred

[Quantum321]

Very good but not quite accurate.

 

A homogeneous and isotropic fluid has equal pressure on every point on an object. So as the volume changes this relationship still holds on expansion.

 

The object gains no inertia as the sum of force in any direction equals zero. This however doesn't prevent the volume from changing between two objects.

 

The objects themself do not move but the distance between them change due to volume change.

Correlating this back to pressure we can accurately express that expansion is not due to pressure as their is no pressure gradient to cause a flow. However pressure can still perform the work for expansion.

 

This is where it differs in your room example. In the case of expansion it modelled as an adiabatic solution. (no net inflow or outflow).

 

This is also why superluminal expansion does not violate GR. As it is not an inertial change.

 

"The objects them self do not move but the distance between them change due to volume change." I see what you're saying. Not sure I buy into this...lol

[Strange]

 

Hello Mordred, I guess you're right. He also said the warping of space-time was gravity. Its only one term in the equation of gravity. It's a small factor.

 

 

I don't think I can let that pass.

 

GR describes gravity as the curvature of spacetime. There is no "other factor".

[Mordred]

Lets try and fill in some details on Inflation. The particular example I will use is one I believe most strongly in out of the 73+ viable inflation models.

 

Higg's inflation.

 

Higg's field. Is a complex scalar field [latex]SU(2)_w[/latex] doublet.

 

[latex]\phi=(\begin{matrix}\phi_1 & \phi_2 \\ \phi_3& \phi_4 \end{matrix})[/latex]

 

the vector bosons (guage bosons) interact with the four real components [latex]\phi_i[/latex] of the [latex]SU(2)_{w^-}[/latex] symmetric field [latex]\phi[/latex]

 

false vacuum corresponds to [latex]\phi=0 or \phi_1=\phi_2=\phi_3=\phi_4=0[/latex]

 

the true vacuum corresponds to [latex]\phi_1=\phi_2,,,\phi_3^2=\phi_4^2=constant>0[/latex]

 

 

assign V on the Y axis, [latex]\phi_3[/latex] on the x axis, [latex]\phi_4[/latex] on a 45 degree between the x and Z axis.

 

when you have conditions [latex]\phi_4=0,\phi_3>0[/latex] then the rotational symmetry is spontaneously broken. The Higg's boson becomes massive as well as the vector bosons W+,W-Z and photons

 

the two neutral fields [latex]B^0 and W^0[/latex] form the linear combinations

 

[latex]\gamma=B^0 cos\theta_w+W^0sin\theta_w[/latex]

[latex]Z^0=-B^0sin\theta_w+W^0cos\theta_w[/latex] where Z becomes massive. whee as our ordinary photon [latex]\gamma[/latex] remains massless as the photon does not interact with the electro-weak Higg's field. It is electro-weak neutral.

 

The electroweak symmetry is given by [latex]SU(2)_w\otimes U(1)_{b-L}[/latex]

 

as time decreases the vacuum expectation value [latex]\theta_0[/latex] decreases. (expansion in reverse) the true minimal of the potential is [latex] \phi=0[/latex] this occurs above the critical temperature

 

[latex]T_c=\frac{2\mu}{\sqrt{\lambda}}[/latex] at this point the field interactions take on in essence superconductivity properties.

OK here is some Higg's field details that will make understanding the Higg's itself simpler. Keep in mind I am using Lewis Ryder "Introductory to General Relativity" for this. You may find more recent articles with slightly different metrics. (PS this will take me some time to type in and latex)

 

First we need to notice that there is actually 4 field quanta in electro-weak theory. [latex]\gamma, W^-, W^+, and, Z^o.[/latex] notice the second and third is an antiparticle pair.

 

Now the problem is we need a mechanism to give the neutrinos mass without giving photons mass. This is where the Higg's mechanism steps in.

To start with Peter Higg's looked at superconductivity. The defining characteristic of conductivity is that at a temperature below a critical temperature [latex]T_c[/latex] some metals lose all electrical resistance. Resistance literally becomes zero, not merely very small.

 

[latex](E=Rj) =j=\sigma E[/latex]

 

where [latex]\sigma[/latex] is the conductivity. A metal in conductivity state then exhibits a persistant current even in no field:[latex]j=\not=0[/latex] when E=0. The key to understanding superconductivity is to describe the current as supercurrent [latex]j_s[/latex]. But unlike the equation above to realize this is proportional not to E but to the vector potential A.

[latex]j_s=-k^2A[/latex] with a negative proportionality. This is the London equation.

 

The relevant property we however are seeking is the Meissner effect, which is a phenomena that the magnetic flux is expelled from superconductors.

 

Higg's then showed that suitably transformed into a relativistic theory, this is the equivalent to showing the photon has mass. (just not rest mass lol)

 

The reasoning goes as follows. First thee London equation explains the Meissner effect, for taking the curl of Amperes equation

[latex]\nabla*BB=j[/latex] gives [latex]\nabla(\nabla^2B=\nabla*j[/latex] noting that [latex]\nabla*B=0[/latex] (no magnetic monopoles) gives [latex]\nabla^2B=k^2B[/latex] which is equal to [latex]\nabla^2A=k^2A[/latex]

In one dimension the solution to this is

 

[latex]B(x)=B(0)exp(-kx)[/latex]

which describes the Meissner effect-the magnetic field is exponentially damped inside the superconductor, only penetrating to a depth of order 1/k.

 

This however is still non relativistic. To make it relativistic [latex]\nabla^2[/latex] is replaced by the Klein_Gordon operator [latex]\Box[/latex] and A by the four vector [latex]A^\mu=(\phi,A)[/latex]

 

giving

[latex](\frac{1}{c^2}\frac{\partial^2}{\partial t^2}+\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}+\frac{\partial^2}{\partial x^2})A^\mu=k^2A^\mu[/latex]

 

the vector potential is a field but we are currently interested in the photon, the quantum of the field. so we make the transition to quantum theory by the usual description.

[latex]\frac{\partial}{\partial t}\mapsto-\frac{i}{\hbar}E, \frac{\partial}{\partial}{\partial x}\mapsto\frac{i}{\hbar p_x}....[/latex]etc

 

giving the quantum of the field [latex]A^\mu[/latex],

[latex]E^2-p^2c^2=k^2c^2\hbar^2[/latex]

 

where E is the total, including rest energy of the field quantum an p isits momentum comparison to [latex]E^2-p^2c^2=m^2c^4[/latex] implies that the mass of the quantum in a superconductor is

[latex]m_\gamma=\frac{k\hbar}{c}[/latex] the photon behaves as a massive particle in a superconductor. This is the import of the Meissner effect.

 

Now we need to make a further connection to the Bardeen-Cooper_Schreiffer (BCS theory) of superconductivity which is a microscopic theory that accounts for superconductivity by positing a scalar field [latex]\phi[/latex] (spin zero for scalar fields). Which describes a Cooper pair of electrons, the pairing is in momentu space rather than coordinate space. You can correlate the many particle wave function of Cooper pairing with the above. I'm trying to save time here lol and this is already getting lengthy.

 

The main difference between a superconductor and the Higg's field is that the Higg's field is all pervasive unlike (unlike BCS which is inside a superconductor)

 

The Higg's field through treatment gives rise to the mass of the above neutrinos in the same manner but not to photons. In point of detail the Higg's field can be treated as 4 separate fields one for each of the above. latex]\gamma, W^-, W^+, and, Z^o.[/latex]

 

Now the Higg's potential when [latex]t<t_c[/latex] has a maximum at [latex]\phi=0[/latex] and two minima at [latex]\phi=\pm A[/latex] when[latex] t>t_c][/latex] there is only a minimal at [latex]\phi=0[/latex] THIS is the Mexican hat potential.

 

[latex]V \phi=\frac{m^2}{2}\phi^2+\frac{\lambda}{4}\phi^4[/latex] where [latex]\phi^4[/latex] is the quartic self interaction.. The extremal values of [latex]V\phi[/latex], given by [latex]\partial V/\partial \phi=0[/latex] becomes

 

[latex]\phi=0,\pm\sqrt{\frac{-m^2}{\lambda}}=0,\pm a[/latex]

 

when there is no field [latex]\phi=0[/latex], the energy is not a mimimal but at a maximal, further more the lowest energy is a state in which the field does not vanish and is also two fold degenerate.

 

I hope that helps better understand the Higg's field and how it came about ie was derived in the first place. Section 10.10 Lewis Ryder "Introduction to General Relativity"..

 

You can see from this that as the field strength changes via the meta stability the mass values will also be influenced.

 

 

Scalar field Dynamics here we need to couple the scalar field to gravitation.

 

[latex]\frac{1}{2}\dot{\phi}^2+\frac{1}{2}(\triangledown\phi^2)+V(\phi)[/latex]

 

and the dynamics can be described by two equations. ::Friedmann equations

 

[latex]H^2+\frac{k}{a^2}=\frac{8\pi}{3M^2_P}(\frac{1}{2}(\dot{\phi})^2+V(\phi)[/latex]

 

and the Klein Gordon equation obeys the scalar fields [latex]\ddot{\phi}+3H\dot{\phi}+\acute{V}(\phi)=0[/latex]

 

if the [latex]\phi_a[/latex] is large we have [latex](\triangledown \phi_a^2)<<V(\phi_2)[/latex]

 

the speed of expansion [latex]H=\frac{\dot{a}}{a}[/latex] is dominated by the potential [latex]V(\phi_a)[/latex] in equation

 

[latex]H^2+\frac{k}{a^2}=\frac{8\pi}{3M^2_P}(\frac{1}{2}(\dot{\phi})^2+V(\phi)[/latex]

 

the advantage of Higg's inflation is that inflation is readily modelled using just the standard model of particles. We do not need k-Fields, inflatons, curvatons, Quintessence or any other quasi particle or field.

 

Secondly we can model inflation as a symmetry phase transistion which is extremely important as we tie inflation with the electro-weak symmetry breaking itself

Edited November 28, 2016 by Mordred

[Mordred]

Higg's Field, GR and the FLRW.

 

[latex]R_{\mu\nu}-\frac{1}{2}[/latex] with c=1

here [latex]T_{\mu\nu}[/latex] is the stress energy-momentum tensor. In general one has to consider all contributions from all possible fields. So lets start with the electromagnetic contributions.

 

[latex]T_{\mu\nu}^{em}=(4\pi)^{-1}(-F_\mu^\alpha F_{v\alpha}+\frac{1}{4}g\_{mu\nu}F_{\alpha\beta}F^{\alpha\beta})[/latex]

 

where the electric field tensor [latex]F_{\mu\nu}[/latex] is given by four potential [latex]F_{\mu\nu}=A_\mu-A_{v\mu}[/latex] [latex]A_\mu[/latex] being the four potential.

 

when we introduce the scalar field for Higg's [latex]\phi[/latex] we need to add an additional energy momentum tensor on the RHS. Without going into excessive detail on the Langevians which I will skip. We get the following energy tensor.

 

[latex]\acute{T}_{\mu\nu}=\partial_\mu\phi\partial_v\phi-g_{\mu\nu}L=\partial_\mu\phi\partial_v\phi-g_{\mu\nu}[\frac{1}{2}\partial_\sigma\phi\partial^\sigma\phi-V(\phi)][/latex]

 

we can write the stress tensor [latex]T^v_\mu=diag(\epsilon,-p,-p,-p)[/latex] with the prime tensor [latex]\acute{T}^v_\mu=diag(\acute{\epsilon},-\acute{p},-\acute{p},-\acute{p})[/latex]

 

[latex]\acute{\epsilon}=\frac{1}{2}\dot{\phi}^2+V(\phi);;\acute{p}=\frac{1}{2}\dot{\phi}^2-V\phi;;\\dot{\phi}=\frac{\partial\phi}{\partial t}[/latex]

 

this shows that we can simply replace [latex]\epsilon[/latex] with [latex]\acute{\epsilon}+\epsilon[/latex] and p by [latex] \acute{p}+p[/latex]

 

so the following holds

 

[latex]\frac{\dot{R}}{R}=H^2=(\frac{8\pi}{3})(\epsilon+\acute{\epsilon})[/latex]

 

[latex]2\frac{\dot{R}}{r}+H^2=-8\pi G(p+\acute{p})[/latex]

 

This should be enough detail on how the Higg's field works in regards to expansion contributions. The last two equations provide its influence upon the volume elements.

 

Enjoy lol

 

PS yes the above is math heavy, however we can see how the Higg's field is modelled by the above with its stress tensor contributions. This last section many will find handy as we just added multiple field couplings to gravity. I demonstrated how a spin 1 field (electromagnetic) couples to the spin 2 field (gravity) as well as how a spin (zero) scalar field couples to spin (2) gravity.

 

Not something that is easy to find examples of.

 

Adding SU(3) for the chromodynamics follows similar procedures, (strong force) again its spin 1 but has additional degrees of freedom. Which affects the energy-momentum tensor

Edited November 28, 2016 by Mordred