A Thought Experiment and a Question

G

gluon

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I have a question concerning the Uncertainty Principle, and the energy density of the vacuum. To explain this better, i created a thought experiment.

In a dense liquidic solution, whether being very dense or not very dense, exerts a (uniform - if in the center of a gravitational field) pressure on a materials surface that are submerged. So if you submerged a marble in a bowl of water, the pressure of the water when submerged will be tense upon the surface of the object.

I now speculate the nature of spacetime, and treat it as being fluidlike; in many ways it is fluidic, as matter distorts spacetime round it and drag it with it, much like the viscosity of water drag. I wonder about a particle being being akin to a system submerged in a dense fluidlike system, where the particle is affected by a pressure exerted on it equally because of the energy density of the vacuum.

Wouldn't such a force exerted on particles not try and locate particles to a specific area of spacetime and make its momentum even more uncertain?
 
The pressure on an object inserted into a liquid in a gravitational field is NOT uniform, but varies by depth, and this effect is important -- it gives us the buoyancy of materials in liquids.

Solid objects, immixable liquids and gases displace liquids, but solid matter, etc does not displace space-time. Your analogy with viscosity cannot be made exact in any experimental situation. (That's an open-ended challenge to establish an actual scaling experiment that at all scales gives the same measure of "viscosity" of space time.) Pressure has a direction which is normal to the surface of the object and which varies by depth, but in what dimension is your "space-time pressure" and what does depth correspond to with respect to the energy density of the vacuum?

Until you demonstrate that this analogy is more than just empty words that don't connect to each other, your final sentence is meaningless.
 
rpenner said:
The pressure on an object inserted into a liquid in a gravitational field is NOT uniform, but varies by depth, and this effect is important -- it gives us the buoyancy of materials in liquids.

Solid objects, immixable liquids and gases displace liquids, but solid matter, etc does not displace space-time. Your analogy with viscosity cannot be made exact in any experimental situation. (That's an open-ended challenge to establish an actual scaling experiment that at all scales gives the same measure of "viscosity" of space time.) Pressure has a direction which is normal to the surface of the object and which varies by depth, but in what dimension is your "space-time pressure" and what does depth correspond to with respect to the energy density of the vacuum?

Until you demonstrate that this analogy is more than just empty words that don't connect to each other, your final sentence is meaningless.
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I thought it obvious that my analogy required that the object be emersed in an equal depth to the bed. But it was only an analogy to help explain the effects i mean of the energy density of the vacuum on a particle.
 
In what sense does the energy density of the vacuum exert a force on the particle?

As I have told you in the past, attempting to extract meaning from the zero point energy is pretty difficult, and a lot of smart people have tried and failed to assign any real meaning to the quantity. All attempts to do so end in a catastrophic disagreement with experiment.
 
BenTheMan said:
In what sense does the energy density of the vacuum exert a force on the particle?

As I have told you in the past, attempting to extract meaning from the zero point energy is pretty difficult, and a lot of smart people have tried and failed to assign any real meaning to the quantity. All attempts to do so end in a catastrophic disagreement with experiment.
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Scientists like mathematician and prof. john barrow, believes the energy density of the universe affects the motion of matter (just like a drag force) $$\Phi \Lambda$$ is not in fact zero, as Einstein had believed. In fact, the Casimir Force has been proven experimentally, and just recently, a positive Casimir Force has been detected by changing the experimental plates to one being made of silicon. So, as many scientists keep roporting - it seems that the Dirac Sea correctly predicts hidden virtual particles that are in the vacuum interacting with real matter under $$\Delta E \Delta t>\frac{h}{2}$$ the uncertainty in energy and time, which allows a particle to pop into existence with an undefined energy, allowing superluminal properties.

So the force exerted on a system in this vacuum, will be analogous to the system in the fluid, as there will be a density of force applied on the surface of the said system. So the force acting homogenously over it is by definition the vacuum energy.
 
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gluon said:
So the force exerted on a system in this vacuum, will be analogous to the system in the fluid, as there will be a density of force applied on the surface of the said system. So the force acting homogenously over it is by definition the vacuum energy.
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Where is the surface of the electron located? Of the photon? Of the proton, even?
 
BenTheMan said:
Where is the surface of the electron located? Of the photon? Of the proton, even?
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If you pardon for a moment to reitterate passages from another thread, there is real problem concerning ''a surface'' to an electron. It seems that the question of whether an electron has a structure is not definate yet. Currently we are dealing (as you well know Ben) with the idea of spin being angular momentum, but then that would mean that the particle cannot have a definate mass. But if it contains a very small volume, then a density can be calculated (taking into respects the relativistic energy changes and mass density).

As i said, in the Dirac Model, the electron is found to be massless when at complete rest, which made use also of spin, which would hve left every spin 1/2 particle (and even integer spins) a peice of matter which cannot ever be at rest. Even when stationary without any change in inertia, a particle would always be in movement.

So the pressure (or stress energy) on the system's surface, also depends on whether it even has a surface area. I would bet there is, and if there is, (albiet as small as it is), there is a natural pressure on its position in respect to the density of the vacuum.
 
I thought we were discussing pressure -- aka force per unit area perpendicular to a surface.
 
(If there is a wall of density, then the energy which is evidently locating the particle down, could find itself constantly wanting to tunnel through spacetime.)

I also imagine that a particle trying to move through this energy density $$\Lambda$$ would cause a distortion in the Dirac Sea (or if you wish, the Zero-Point Field), just as much as a photon $$p^{\mu}p_{mu}=0$$ with momentum $$E=p^2c^2+M^2c^{2.2}$$ distorts the fabric of space and time and can then couple to the gravitational field. So matter (with a real surface spin) would distort the zero-point field all the time, and excite the energy in a slice of spacetime; this seems to go well with experimentation, since the presence of matter at small levels can excite vacuum energy into existence, containing a very small amount of negative matter!
 
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"I now speculate the nature of spacetime, and treat it as being fluidlike; in many ways it is fluidic, as matter distorts spacetime round it and drag it with it, much like the viscosity of water drag. I wonder about a particle being being akin to a system submerged in a dense fluidlike system, where the particle is affected by a pressure exerted on it equally because of the energy density of the vacuum."

What would be your thoughts on replacing spacetime with that old-chestnut aether? Some scientists (unfortunately labelled for the most part crackpots) believe aether to be the vacuum energy. Of course, this might be asking a bit much, unless you're willing to question whether it's possible that time does not exist. If you are, then the aether quite easily fills the boots of spacetime.
 
gluon said:
Indeed, what i am talking about is the vacuum energy, and the pressure it exerts on a particles position in spacetime.
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How does this work? Can you calculate the pressure? What does it mean?

If you can't answer these questions, this thread cannot remain here. You've made some random analogy that you can't support with reasoning or with calculations. All you seem to be able to do is appeal to authority.
 
gluon said:
As i said, in the Dirac Model, the electron is found to be massless when at complete rest
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When trying to BS, don't make specific claims. Because when you do, you're almost invariably wrong. If you had bothered to look up the Dirac equation anywhere, even Wikipedia, you'd see it involves an m term. It differs from the Klein Gordon equation in that it's only a linear mass term, not quadratics, but there's various reasons for that that I won't bother going into. Suffice to say, the minutest of research on your part would have made you see you were wrong.
 
AlphaNumeric said:
When trying to BS, don't make specific claims. Because when you do, you're almost invariably wrong. If you had bothered to look up the Dirac equation anywhere, even Wikipedia, you'd see it involves an m term. It differs from the Klein Gordon equation in that it's only a linear mass term, not quadratics, but there's various reasons for that that I won't bother going into. Suffice to say, the minutest of research on your part would have made you see you were wrong.
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You talk about Diracs Equation and the Klein-Gorden Eqution as if i knew nothing about it. If you read over my posts again, it was because i was investigating the Dirac Electron in which i found information which explained the electron could be massless at rest if spin was a physical spin. If the electron has mass and spins a real rotational spin, if being pointlike requires a spin being faster than the speed of light, i do believe, twice as fast because of the half-integer spin.

And by the way, don't you mean why the Klein Gorden is a linear energy-momentum-mass term. ;)
 
The half integer 'spin' of most fermions doesn't mean something is spinning, it is called that because the generators of the effect have the same Lie algebra as the more commonly understood 'angular momentum'. It's called spin because it's mathematical akin to classical rotating, just as the strong charge is called 'colour' because there's 3 of them and they add to being colourless. Doesn't mean quarks are red, green and blue or that electrons are little spheres spinning on an axis.

And the Klein Gordon equation has a quadratic term in the mass, since it's of the form $$(\partial^{\mu}\partial_{\mu}-m^{2})\phi = 0$$, while the Dirac equation is $$(\gamma^{\mu}\partial_{\mu}-m)\psi = 0$$, up to choices in notation and signature. The Dirac equation involves matrices because it's the only way to find an operator, $$D_{S}$$ such that $$D_{S}^{2}$$ is the Klein Gordon operator, so that fermions also obey wave properties. There's a huge chunk of differential geometry and operator theory relating to the Dirac operator, because its the operator which squares to the Laplacian (with or without mass is dependent on the system of interest).

Reiku, don't play games you know you won't win.
 
AlphaNumeric said:
The half integer 'spin' of most fermions doesn't mean something is spinning, it is called that because the generators of the effect have the same Lie algebra as the more commonly understood 'angular momentum'. It's called spin because it's mathematical akin to classical rotating, just as the strong charge is called 'colour' because there's 3 of them and they add to being colourless. Doesn't mean quarks are red, green and blue or that electrons are little spheres spinning on an axis.

And the Klein Gordon equation has a quadratic term in the mass, since it's of the form $$(\partial^{\mu}\partial_{\mu}-m^{2})\phi = 0$$, while the Dirac equation is $$(\gamma^{\mu}\partial_{\mu}-m)\psi = 0$$, up to choices in notation and signature. The Dirac equation involves matrices because it's the only way to find an operator, $$D_{S}$$ such that $$D_{S}^{2}$$ is the Klein Gordon operator, so that fermions also obey wave properties. There's a huge chunk of differential geometry and operator theory relating to the Dirac operator, because its the operator which squares to the Laplacian (with or without mass is dependent on the system of interest).

Reiku, don't play games you know you won't win.
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Much more easier said, albiet simpler, is that if we take the spin of the electron, manipulate it, so that it will rotate $$360$$ degrees and brought finally back to orientation. Now, you would think that the $$360$$ degree spin forward, would be the same as the common unrotated electron, because $$360$$ degrees means a full circle. But it turned out that only atoms with a multiple integer of $$\frac{h}{2\pi}$$ will be able to arrive at the same location. This is quantized angular momentum. However, the results for all $$\frac{1}{2}$$-spin particles ''fermions,'' would need to move another $$360^2$$ degrees just to arrive at the same location. This obviously goes for all fermions... protons... neutrons ect.
 
gluon said:
... if being pointlike requires a spin being faster than the speed of light, i do believe, twice as fast because of the half-integer spin.
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Can you explain me how can a spin be faster than the speed of light.
 
1100f said:
Can you explain me how can a spin be faster than the speed of light.
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Well, it can't. Unless it is pointlike, and has a rotational spin, then it would need to have a spin faster than the speed of light, due to the orientation of quantum particle spin! But either spin is not a real rotational spin, or the equations that describe the relationships refer to an angular momentum, which is quite popular right now.
 
gluon said:
... it would need to have a spin faster than the speed of light...
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Please explain me how can a spin (which has dimension [M][L]^2/[T]) be faster than the speed of light (which has dimension [L]/[T]). It is like saying that the color of a crocodile is larger than its weight.
 
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