"Something was created from nothing"
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05-08-2014, 02:24 PM
RE: "Something was created from nothing"
(05-08-2014 01:32 PM)Stevil Wrote:  The position of an electron is based on its probability function, not based on the path being unobscured. The probability is a wave function which goes from positive to negative and has nodes on the 0, These zeros give us zero probability that the electron will be at that position. But this doesn't stop the electron from going from the positive to the negative it just skips the zero position.
Also of course, energy is quantised so certain states are impossible.

Yes; the probability amplitude (what's measured) is the magnitude of the probability density function at any point in spacetime. Wave functions exist in position/momentum space; each waveform possesses a discrete energy. While the probability amplitude is technically real-valued for all free space (up to the limit of the quantisation of free space itself), the energy levels are much more visibly quantised.

The higher-order interactions and statistical dynamics smear the nice abstract comb function, though. So we get bands of energies - and if you line those up right you get semiconductors, like that fine computer you're using right now.

(05-08-2014 01:32 PM)Stevil Wrote:  Because electrons don't traverse a continuous path then this allows them to "go through" barriers that would otherwise be impossible for them to go through. This is called quantum tunnelling. Without this, Stars would not shine.

Yes; nuclear fusion requires that nuclei be so close together that the region is classically forbidden.

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05-08-2014, 04:00 PM
RE: "Something was created from nothing"
(05-08-2014 02:24 PM)cjlr Wrote:  the probability amplitude (what's measured) is the magnitude of the probability density function at any point in spacetime. ...
gotta say, It's great to have knowledgeable scientists making valuable contributions here at TTA.
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05-08-2014, 05:33 PM
RE: "Something was created from nothing"
(05-08-2014 02:15 PM)cjlr Wrote:  
(05-08-2014 01:09 PM)Michael_Tadlock Wrote:  I don't understand. Don't "connected observable interactions" lead to entropy? How could entropy accelerate faster or slower than the interactions of objects and particles?

Not all interactions require an increase in entropy. The laws of thermodynamics only say that net entropy change is greater than or equal to zero. There are many interactions which - in isolation, that's the tricky part - do not exhibit a change in entropy (trivial example: an elastic collision in a vacuum).

We can actually perform nearly entropy-neutral processes, but to that's only by "isolating" a system via an outside energy input (ie thermal and electrodynamic shielding - but we can't block gravity). So in our experience isentropic analysis is a theoretical convenience.

(05-08-2014 01:09 PM)Michael_Tadlock Wrote:  This is my understanding of what a vacuum fluctuation is; essentially two particles, a matter particle and an anti-matter particle, nearly instantaneously come into existence and then annihilate each other. If I am understanding you then, the annihilation part, and the popping into existence part, don't happen in a particular order; that they are interchangeable. I am reminded of the "chicken and the egg" problem.

I don't understand its implications. What does this imply about time?

It implies that time is an emergent (and contingent) phenomenon.
(see here)

They happen in a particular order from our observation because they are happening within the same spacetime framework we're in - they're occurring in a relatable reference frame.

But that pair-annihilation is not intrinsically time-ordered. Reversing the symmetries involved reveals the particle to be an antiparticle travelling "backwards" in time and vice versa. Either way, the initial and final state are indistinguishable.

(05-08-2014 01:09 PM)Michael_Tadlock Wrote:  Right, because gravity (negative energy) and matter (positive energy) cancel eachother out, and vacuum fluctuations annihilate each other leaving zero net total energy.

Indeed.

I think I get it. With the universe having zero net total energy, it is possible that we emerged by the same properties that create and destroy quantum fluctuations. Time then, our time, would be internal to the system. You are suggesting that if you could observe the universe at the moment before the "bang", that you might see nothing. The entire life of our universe would be relative to the universe, anything outside it would only see a static point. This is very interesting. I haven't come across this before.

One bit that still bothers me.

Quote:Not all interactions require an increase in entropy. The laws of thermodynamics only say that net entropy change is greater than or equal to zero. There are many interactions which - in isolation, that's the tricky part - do not exhibit a change in entropy (trivial example: an elastic collision in a vacuum).

If entropy is constant, than on average it would be a linear function of all interactions, wouldn't? Or am I still missing something.
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05-08-2014, 06:11 PM
RE: "Something was created from nothing"
(05-08-2014 02:24 PM)cjlr Wrote:  
(05-08-2014 01:32 PM)Stevil Wrote:  The position of an electron is based on its probability function, not based on the path being unobscured. The probability is a wave function which goes from positive to negative and has nodes on the 0, These zeros give us zero probability that the electron will be at that position. But this doesn't stop the electron from going from the positive to the negative it just skips the zero position.
Also of course, energy is quantised so certain states are impossible.

Yes; the probability amplitude (what's measured) is the magnitude of the probability density function at any point in spacetime. Wave functions exist in position/momentum space; each waveform possesses a discrete energy. While the probability amplitude is technically real-valued for all free space (up to the limit of the quantisation of free space itself), the energy levels are much more visibly quantised.

The higher-order interactions and statistical dynamics smear the nice abstract comb function, though. So we get bands of energies - and if you line those up right you get semiconductors, like that fine computer you're using right now.

(05-08-2014 01:32 PM)Stevil Wrote:  Because electrons don't traverse a continuous path then this allows them to "go through" barriers that would otherwise be impossible for them to go through. This is called quantum tunnelling. Without this, Stars would not shine.

Yes; nuclear fusion requires that nuclei be so close together that the region is classically forbidden.

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06-08-2014, 08:45 AM
RE: "Something was created from nothing"
(05-08-2014 05:33 PM)Michael_Tadlock Wrote:  I think I get it. With the universe having zero net total energy, it is possible that we emerged by the same properties that create and destroy quantum fluctuations.

Yes, broadly speaking.

(05-08-2014 05:33 PM)Michael_Tadlock Wrote:  Time then, our time, would be internal to the system. You are suggesting that if you could observe the universe at the moment before the "bang", that you might see nothing. The entire life of our universe would be relative to the universe, anything outside it would only see a static point. This is very interesting. I haven't come across this before.

I haven't watched the videos linked upthread, but that is not an uncommon line of thought in physics, so they may mention it.


(05-08-2014 05:33 PM)Michael_Tadlock Wrote:  If entropy is constant, than on average it would be a linear function of all interactions, wouldn't? Or am I still missing something.

Entropy is a trace over logarithms, not a linear function...

Microscopically it reflects disorder - the number of microstates and their occupation probabilities. "Order" indicates the existence of energy gradients (non-random configurations). Classical thermodynamics, quantum mechanics, and information theory all more or less converged on equivalent definitions.

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06-08-2014, 01:37 PM
RE: "Something was created from nothing"
(06-08-2014 08:45 AM)cjlr Wrote:  Entropy is a trace over logarithms, not a linear function...
http://en.wikipedia.org/wiki/Boltzmann%2...py_formula
S=k.log W
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06-08-2014, 01:49 PM
RE: "Something was created from nothing"
(06-08-2014 01:37 PM)Stevil Wrote:  
(06-08-2014 08:45 AM)cjlr Wrote:  Entropy is a trace over logarithms, not a linear function...
http://en.wikipedia.org/wiki/Boltzmann%2...py_formula
S=k.log W

Only under a variety of approximations, involving equal occupation probabilities and diagonal bases (ie, no correlation functions). The full form for classical entropy is S = k.sum(p.ln(p)).

Under quantum statistics, the expression is S = k Tr(p.ln(p)), Tr() being the matrix trace of density operators p. In the right conditions this reduces to the classical form as expected (since quantum mechanics is a superset of classical mechanics, the appropriate limiting forms of quantum expressions should reproduce their classical antecedents).

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