Author Topic: Here is the actual math for the Dirac equation (relativistic quantum electron)  (Read 2171 times)

Offline Baruch

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Notice that this applies, to a single electron, your universe consists of a single electron in isolation (no measurement).  Not a realistic condition.

So to make it more realistic, we can start with a single electron moving in an EM field (Quantum Electrodynamics).  To apply it further, to the EM field itself we get Relativistic Quantum Field Theory.  One comeuppance is that an election in a EM field, moving relativistically, can't have a single trajectory, because of QM or because of Relativity, but the combination means that it can't even be a single electron, but an infinity of them (many worlds theory).  The problem with quantum gravity, is that the Pythagorean equation ain't exact anymore, but approximate (because of space-time curvature).

The Dirac equation by assumptions, only works in a flat space-time, so without gravity.  But Einstein showed that Special Relativity wasn't consistent, without General Relativity.  This means that the Dirac Equation in some subtle way, isn't self consistent (in all circumstances).  It works plenty well in many circumstances (but has to be solved numerically, not in closed form) ... remember in this first video, that the energy of the election has become an infinite series.

The whole series for the Dirac Equation is in 3 parts.
« Last Edit: January 05, 2018, 05:46:56 PM by Baruch »
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Offline Cavebear

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Notice that this applies, to a single electron, your universe consists of a single electron in isolation (no measurement).  Not a realistic condition.

So to make it more realistic, we can start with a single electron moving in an EM field (Quantum Electrodynamics).  To apply it further, to the EM field itself we get Relativistic Quantum Field Theory.  One comeuppance is that an election in a EM field, moving relativistically, can't have a single trajectory, because of QM or because of Relativity, but the combination means that it can't even be a single electron, but an infinity of them (many worlds theory).  The problem with quantum gravity, is that the Pythagorean equation ain't exact anymore, but approximate (because of space-time curvature).

The Dirac equation by assumptions, only works in a flat space-time, so without gravity.  But Einstein showed that Special Relativity wasn't consistent, without General Relativity.  This means that the Dirac Equation in some subtle way, isn't self consistent (in all circumstances).  It works plenty well in many circumstances (but has to be solved numerically, not in closed form) ... remember in this first video, that the energy of the election has become an infinite series.

The whole series for the Dirac Equation is in 3 parts.

Gravity matters.  And as you yourself say, the Dirac Equation isn't self-consistent.  And electrons aren't infinite.  Things that don't make sense don't make sense.

I recall when I was taking Astronomy 101 in 1968, I told the Professor that I didn't see how galactic spiral arms could exist as the galaxy revolved.  He dismissed me, saying that they moved so slowly that there hadn't been time for them to collapse the arms. 

Guess who was wrong?
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Offline Baruch

Galaxy arms are more of a wave thing, not a arm thing.  There are physical impacts moving out from the galactic core all the time (giant black hole).  Next one gets to us, we are toast.
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Offline Cavebear

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Galaxy arms are more of a wave thing, not a arm thing.  There are physical impacts moving out from the galactic core all the time (giant black hole).  Next one gets to us, we are toast.

Um "no".  Last I read, spiral galaxy arms are held in place by dark matter, which completely overwhelmes all normal matter gravitationally.
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Offline Baruch

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Um "no".  Last I read, spiral galaxy arms are held in place by dark matter, which completely overwhelmes all normal matter gravitationally.

Speculation.  You have dark matter between the ears ;-)
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There's also Wheeler's idea that the universe really only has one electron:


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I'm waiting for Trump to say: "We could easily stop all the wildfires from happening just by removing all the oxygen from the atmosphere."

Offline Cavebear

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There's also Wheeler's idea that the universe really only has one electron:


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That one is too much for me.  Apparently, I have a dark matter banana in my ear...
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Is that a dark matter banana in your ear, or are you glad to see me?

:)
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I'm waiting for Trump to say: "We could easily stop all the wildfires from happening just by removing all the oxygen from the atmosphere."

Offline Cavebear

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Is that a dark matter banana in your ear, or are you glad to see me?

:)

Hey?  What?   Sorry, I have a dark banana meteorite in my ear.
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Offline Baruch

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There's also Wheeler's idea that the universe really only has one electron:


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That comes from Feynman diagrams.  It easily explains why all electrons are alike ;-)

It would only work, if there was almost exactly the same amount of anti-matter as matter ... and we don't see that.  Dr Alfven ... a plasma physicist, tried to get around this, by saying that there must be much anti-matter out there, even anti-galaxies.  The unsymmetrical decay of K-mesons discovered in the 1960s, pretty much explains why there is so little anti-matter ... basically there could have been equal amounts early in the Big Bang, but by the time hydrogen became neutral, the asymmetry had made sure that almost all of it had decayed into ordinary matter.

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« Last Edit: February 02, 2018, 07:13:26 PM by Baruch »
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Offline Cavebear

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That comes from Feynman diagrams.  It easily explains why all electrons are alike ;-)

It would only work, if there was almost exactly the same amount of anti-matter as matter ... and we don't see that.  Dr Alfven ... a plasma physicist, tried to get around this, by saying that there must be much anti-matter out there, even anti-galaxies.  The unsymmetrical decay of K-mesons discovered in the 1960s, pretty much explains why there is so little anti-matter ... basically there could have been equal amounts early in the Big Bang, but by the time hydrogen became neutral, the asymmetry had made sure that almost all of it had decayed into ordinary matter.

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I thought the idea was that there were (for random causes) like a billion (to the whatever) matter atoms and a billion (to the whatever) minus one anti-matter atoms and what was left was matter.  Of course, had it been the other way around, we would still consider that "matter". 

But that was before dark matter and dark energy...
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Offline Hakurei Reimu

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I thought the idea was that there were (for random causes) like a billion (to the whatever) matter atoms and a billion (to the whatever) minus one anti-matter atoms and what was left was matter.  Of course, had it been the other way around, we would still consider that "matter". 

But that was before dark matter and dark energy...
This is exactly right. The one-electron/proton/neutron theory would require there to be almost exactly as much antimatter in the universe as there is matter. However, we don't seem to find it in sufficient quantity to make the theory viable. Even if we called matter antimatter and vice versa, it doesn't matter — in order for the theory to fly, you need to have them in about equal in quantity, which we don't find anywhere.

Though how Baruch thinks that the Dirac Sea implies infinite worlds is beyond me, because it doesn't.
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Offline Baruch

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This is exactly right. The one-electron/proton/neutron theory would require there to be almost exactly as much antimatter in the universe as there is matter. However, we don't seem to find it in sufficient quantity to make the theory viable. Even if we called matter antimatter and vice versa, it doesn't matter — in order for the theory to fly, you need to have them in about equal in quantity, which we don't find anywhere.

Though how Baruch thinks that the Dirac Sea implies infinite worlds is beyond me, because it doesn't.

Infinite worlds, comes from the multiverse interpretation of QFT ... which was derived from the Dirac equation.
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Offline Hakurei Reimu

Baruch, the many worlds interpretation of quantum mechanics is not a special implication of the Dirac equation. Any quantum theory that includes superposition that can decohere on observation implies the many worlds interpretation as much as the Copenhagen interpretation. They are both, after all, interpretations of what happens to the quantum system and the universe as the weirdness of the quantum world yields to the classical determinism of the macroworld. Many worlds is not dependent upon nor is implied by QFTs, let alone the Dirac equation specifically.

The other thing is that the concept of a quantum field predated the Dirac equation; the You are not allowed to view links. Register or Login predated the Dirac equation by two years, and Wolfgang Pauli came up with a You are not allowed to view links. Register or Login around the same time.
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Offline Baruch

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Baruch, the many worlds interpretation of quantum mechanics is not a special implication of the Dirac equation. Any quantum theory that includes superposition that can decohere on observation implies the many worlds interpretation as much as the Copenhagen interpretation. They are both, after all, interpretations of what happens to the quantum system and the universe as the weirdness of the quantum world yields to the classical determinism of the macroworld. Many worlds is not dependent upon nor is implied by QFTs, let alone the Dirac equation specifically.

The other thing is that the concept of a quantum field predated the Dirac equation; the You are not allowed to view links. Register or Login predated the Dirac equation by two years, and Wolfgang Pauli came up with a You are not allowed to view links. Register or Login around the same time.

Thanks for adding more detail, but it didn't actually matter.  You simply like to ... add on.  I do too.  Let me know when you get your Nobel Prize or Field Medal, won't you?
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