Can't help thinking: There is too a Spoon!
Or does the sum total of the entire cosmos add up to nothing? -- even such an equation of state by itself is surely something!
Quote:
Top question, and there's the rub. The uncertainties of quantum mechanics for instance are the result of not being able to get outside the system, so randomness is what we see. Probabilities are a way of quantifying the unknowns, and certainty only resides in the past.
Apologies if this is straying off-topic, can't help wondering if there is such a thing in physics :)
Have a gander at Null Coordinates, hopefully it's helpful ...
As far as I can penetrate the maths, it looks like a re-expression of known issues. He rotates the axes of measurement, essentially measuring spacetime events according to a photon's view. Obtaining the not-unusual result that the finite speed of light limits our knowledge of events, specifically matter outside the light cone cannot influence.
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This reminds us of other fundamental relations of physics that have found expression as hyperbolic relations, such as the uncertainty relations
Just because one can derive an inverse relationship ( basically a faster moving object travels a greater distance in a shorter time ) doesn't imply 'uncertainty' in the Heisenberg sense. Actually I'm not real sure what he was getting at - specifically what new prediction/explanation would entail from the axis rotation.
Quote:
Arguably, it is only in the context of Minkowski spacetime, with its null connections between distinct events, that phenomena involving quantum entanglement can be rationalized.
This simply means that because the proper time for a photon is zero ( time doesn't pass at the speed of light ) implies that 'action at a distance' occurs. But the key point is missed : it doesn't matter what a photon experiences, as we're never going to ride one. The 'singularity' he describes is merely that one travels at the speed of light or one doesn't. And because you can't transition between the two ( you either have a rest mass or you don't ) then such viewpoints can never be compared experimentally. Although it might be great to hypothecate what might be an 'outside' view, this doesn't advance our understanding of entanglement.
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Likewise in special relativity we may imagine that there is an absolute and precise relationship between the times of two distant events, but we are prevented from determining it due to the practical limitations. If only we had an infinnitely fast signal, i.e., if only 1/c was zero, we could measure things with infinite precision.
I think he's confusing 'precision' with 'knowledge' here. If something is outside our lightcone it has neither a quantum mechanical value of 'expectation' ( average ) nor 'variance' ( spread about the average ) for us. Heisenberg is talking about variable pairs where mutual variance is constrained. Special relativity talks of whether you have an expectation at all.
An infinite speed of light would give you instantaneous knowledge, but that doesn't mean greater exactness. Quantum mechanical uncertainty doesn't flow from propagation delay. Or if it does, I can't see that his maths illustrates that. Stuff outside the light cone doesn't enter any prediction flowing from the wavefunction! To my knowledge no-one includes tachyons in sum-over-histories integrals. If you could do that, with a prediction that includes effects from said faster-than-light behaviour then you could measure experimentally against that.
Cheers, Mike.
( edit ) The ( special ) relativistic duality is that one can either increase the speed of a body in some frame, OR you can change the speed of the frame. You'll get equivalent descriptions with either, known as a 'Lorentz boost'. Whether this is observed by a sub-light speed observer or one at light speed makes no odds. In the sub-light frame/case you'll get a 'mass shell' curve for energy versus momentum ( where velocity is dE/dP and the energy axis intercept is the rest mass ) and the curves go asymptotically to the light cone. In the null co-ordinates instance you still get the same interpretation.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
Since the light-lines a and b are degenerate, in the sense that the absolute spacetime intervals along those lines vanish, the absolute velocity of a worldline, given by the "slope" db/da = 0/0, is strictly undefined. This indeterminacy, arising from the singular null intervals in spacetime, is at the heart of special relativity, allowing for infinitely many different scalings of the light-line coordinates
(emphasis added) and
Quote:
The relationship between the natural null coordinates of any two worldlines is then expressed by the requirement that, for any given interval dt, the components da,db with respect to one frame are related to the components da',db' with respect to another frame according to the equation (da)(db) = (da')(db').
and also the part right after that: “It follows that the scale factors of any two frames S_i and S_j are related according to
da_i = da_j * sqrt[(1+v_ij)/(1-v_ij)]
db_i = db_j * sqrt[(1-v_ij)/(1+v_ij)]
where v_ij is the usual velocity parameter (in units such that c=1) of the origin of S_j with respect to S_i.â€
(I understand what's meant by a Doppler shift, but not what it means to observe a 'relativistic Doppler shift', say as an up quark interacting with an up & a down quark as in the heart of a proton.) What especially caught my eye was that the terms with the velocity parameter are very close to the 'Gamma2' of this post which came from your idea of a 'separation threshold' and what that might mean for gravity below a certain scale ... so does it seem like there is a basis for the idea of a separation threshold that stems from (how to say it?) being mathematically undefinable or relativistically indeterminate, with regard to the scaling of singular null intervals in spacetime – that is, if the nature of matter is energy and the nature of energy is to be light-like? Am I comparing apples and oranges, or not even in the ballpark? (I know it's a ways from Dark Energy and GWs...)
And when the author remarked on not being able to perform precise measurements, my question was: Is quantum uncertainty and failure of simultaneity one and the same thing (mechanically), then?
Since the light-lines a and b are degenerate, in the sense that the absolute spacetime intervals along those lines vanish, the absolute velocity of a worldline, given by the "slope" db/da = 0/0, is strictly undefined. This indeterminacy, arising from the singular null intervals in spacetime, is at the heart of special relativity, allowing for infinitely many different scalings of the light-line coordinates
(emphasis added) and
This simply means that special relativity doesn't predict a value for the speed of light - that is, the exact ratio between distance and time that photons travel. Special Relativity only says that light has a constant speed, not what that speed might be. You find that out by doing experiments and comparing light's behaviour with respect to your choice of standards ( meters & seconds say ). So if c did have some constant value other than the present one then the discussion remains the same, mutatis mutandis.
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Quote:
The relationship between the natural null coordinates of any two worldlines is then expressed by the requirement that, for any given interval dt, the components da,db with respect to one frame are related to the components da',db' with respect to another frame according to the equation (da)(db) = (da')(db').
and also the part right after that: “It follows that the scale factors of any two frames S_i and S_j are related according to
da_i = da_j * sqrt[(1+v_ij)/(1-v_ij)]
db_i = db_j * sqrt[(1-v_ij)/(1+v_ij)]
where v_ij is the usual velocity parameter (in units such that c=1) of the origin of S_j with respect to S_i.â€
More of the same. In a universe with a different c value a null geodesic is still a null geodesic, but all the velocity dependent effects ( lengths & times ) vary as per the new choice of c. He is implicitly comparing two distinct universes, not relating measurements by different observers in the same universe. He's evidently confused 'frame' with 'universe', and hasn't grasped Special Relativity's principle that c is measured the same regardless of the choice of frame within the universe we inhabit. Specifically : the relativity he is discussing isn't the theory that was defined by Einstein. So he's talking about his own private understanding, or whatever. Which is OK. ( But you need to know that while you read him ).
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(I understand what's meant by a Doppler shift, but not what it means to observe a 'relativistic Doppler shift', say as an up quark interacting with an up & a down quark as in the heart of a proton.) What especially caught my eye was that the terms with the velocity parameter are very close to the 'Gamma2' of this post which came from your idea of a 'separation threshold' and what that might mean for gravity below a certain scale ... so does it seem like there is a basis for the idea of a separation threshold that stems from (how to say it?) being mathematically undefinable or relativistically indeterminate, with regard to the scaling of singular null intervals in spacetime – that is, if the nature of matter is energy and the nature of energy is to be light-like? Am I comparing apples and oranges, or not even in the ballpark? (I know it's a ways from Dark Energy and GWs...)
I guess the problem with handling indeterminates is the following : it doesn't mean you can insert whatever you like, it means you can make no statement. One can misinterpret an old chestnut in logic :
Q. 'what follows from a false statement?'
A. 'anything'
But that means you have no basis to select any particular implication ( that follows from a false predicate ) over any other!
Quote:
And when the author remarked on not being able to perform precise measurements, my question was: Is quantum uncertainty and failure of simultaneity one and the same thing (mechanically), then?
He seemed to be wanting to show that. I don't see that in what he has presented. Perhaps he might be trying to invent/state some sort of many-worlds hypothesis .... sort of the speed of light is different in some 'adjacent' universe from in ours, so that difference then causes what we perceive as quantum uncertainty in this universe? Who can say? :-)
On a semi-related note, I've seen a lecture by Roger Penrose where he discusses what to do at the 'end of the universe'. It would seem that pretty well everything would have decayed by then - protons, neutrons, all manner of exotica, black holes, white holes, wormholes .... except photons ( and maybe some electrons, which worries him ). How are any length/time scales defined? Or put another way, what gives quantum behaviour when there are no interactions? Photons are 'transparent' to one another and there certainly won't be any chance of converting them to even low mass particles. The second law of thermodynamics will have shaved all energy differentials to sweet stuff all ( well below the rest mass of anything ). A scale-less sea of photons ... so what exactly is space & time?
Cheers, Mike.
( edit ) I've re-read that thread you refer to. Fox News does indeed have warped branes ... :-)
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
Thanks for the prompt (and sharp-sighted) reply, Mike.
Quote:
This simply means that special relativity doesn't predict a value for the speed of light - that is, the exact ratio between distance and time that photons travel. Special Relativity only says that light has a constant speed, not what that speed might be.
Yet it has one, very specific and finite, and out of all possible values it seems slow as molasses, practically zero compared to a number like Avogadro's constant, and the volume of a mole of anything is in turn practically nil compared to just the volume of the Earth... Confounding that the speed of light has to be a number that comes from somewhere/when/thing!
I understand what you say about the trouble with handling indeterminates, and appreciate the more proper perspective.
As for time, 14 billion years (about how long since the Big Bang) is practically nil compared to forever – a notion and amount of time that surely must've preceded everything ... ?
After this excursion I should really check to see if Fox News is hiring, feels like I'd fit right in! :))
I think that, in a sense, the classical physicists were right about light. They had an aether which had some 'stiffness' on the one hand ( but was undetectable on the other ). The speed of light was a consequence of that stiffness, obviously by analogy with other wave phenomena. So tension/forces in a material would determine a speed of propagation. For instance loosely coupled particles, like air molecules, would have a certain velocity but strongly coupled atoms in a lattice of iron would be much higher ( speed of sound ).
But I don't think there is an aether. But I do think the speed of light would derivable from some more fundamental understanding of the universe. We call it the 'speed of light' basically because that's the way we have investigated and discovered it historically. In a hypothetical universe where Newton's constant G was much larger, and EM couplings much smaller, then we might be routinely talking of the 'speed of gravity' in everyday life but wondering about detecting electromagnetic waves at specially built detectors - "The Gaser Interferometer EM Wave Observatory" ?! Notwithstanding the question of whether we would exist in such a universe. :-)
So a speed for light would come naturally out of some deeper theory. I do wonder whether field theories are the way to go for that deeper dig. As they were prescribed to get around the 'problem' of action-at-a-distance, they can't really cope with QM entanglement.
It reminds me of a thing called a 'palimpsest', originally meaning a manuscript where the writing had been scraped off and the paper re-used by writing over again. Many of the old classic paintings had this, where there wasn't necessarily a removal attempt, and modern techniques can detect the image layer(s) underneath ( see the later production of The Thomas Crown Affair ). So what we perceive and are is the superficial layer of such a universe which is a palimpsest of sorts. Clearly this is the sort of area indulged in by the extra-dimensionalists like Lisa Randall. The deeper layers in the painting affect the superficial ones, and the trick will be to get a consistent understanding whereby a model of the underlying layer(s) yield observable effects. So entanglement might be explicable, say, and gravity's weakness is because of branes n' bulks n' stuff. Note that a Higg's detection wouldn't change this approach, Higg's is a way of expressing a vacuum property that leads to resistance to motion ie. inertial mass.
Cheers, Mike.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
....In a hypothetical universe where Newton's constant G was much larger, and EM couplings much smaller, then we might be routinely talking of the 'speed of gravity' in everyday life but wondering about detecting electromagnetic waves at specially built detectors -
Cheers, Mike.
Wow ! In this universe, the Seti project “might†have some
The speed of light was a consequence of that stiffness, obviously by analogy with other wave phenomena.
I recall that the speed of light (c) is related to electric permittivity of free space (ε_0) and magnetic permeability of free space (μ_0) with the equation
c = 1 / sqrt(ε_0 * μ_0).
Can it be said that free space has a non-zero value of energy (E) that accompanies the electromagnetic field within it? Regarding a scale-less sea of photons in some near-point-like volume of free space (which said volume has light from all the stars and all the galaxies constantly and continually shining through it, not to mention the presence of a Dirac sea as well), would this not endow free space with an equivalent mass (m) given by
m = E * ε_0 * μ_0
( by substituting the first equation in the equation E = m * c^2 ) ?
Or if not free space then does the electromagnetic field by itself have that mass?
Ah, this is a deep well indeed! Are you thirsty? One must be careful what one asks for ..... :-)
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Quote:
The speed of light was a consequence of that stiffness, obviously by analogy with other wave phenomena.
I recall that the speed of light (c) is related to electric permittivity of free space (ε_0) and magnetic permeability of free space (μ_0) with the equation
c = 1 / sqrt(ε_0 * μ_0).
Yep, that's right. The permeability and permittivity ( while also having way too many syllables ) reflect the effect of static and time dependent charge distributions respectively. They are the constants of proportionality ( or derivable from same ) in Maxwell's equations. So they tell you how much force comes from how much charge and it's movement. If you take Coulomb's Law for a charge and apply the Lorentz transformation then you get two components. A static component that looks like Coulomb's and a velocity dependent part. Magnetism is the latter part, and is really the special relativistic effect of moving with respect to a charge. Or the charge with respect to you, same result either way. Interestingly the initial classical theoretical handling of the scenarios : observer moving, charge stationary vs. observer still, charge moving : were quite distinct explanations in detail, even though the answers yielded were the same in terms of what went where!
Or if you like magnetism is the force arising from where the charge was at some earlier time, accounting for the finite delay in force propagation ( at the speed of light ). So the faster you ( or the charge ) move the more lag you get because of the greater distance you travel in a given time. Sort of like a debt, you pay now or you pay later! You can run but you can't hide! :-)
[ Now the interesting thing that comes out is the direction of the relativistic/magnetic component. If you have two parallel current carrying wires they have a force between them. Not so if perpendicular. All those right-hand rules! ]
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Can it be said that free space has a non-zero value of energy (E) that accompanies the electromagnetic field within it? Regarding a scale-less sea of photons in some near-point-like volume of free space (which said volume has light from all the stars and all the galaxies constantly and continually shining through it, not to mention the presence of a Dirac sea as well), would this not endow free space with an equivalent mass (m) given by
m = E * ε_0 * μ_0
( by substituting the first equation in the equation E = m * c^2 ) ?
Or if not free space then does the electromagnetic field by itself have that mass?
In free space, meaning when there is 'nothing' intervening between two charges those constants have a certain value. Within a given material, gas/liquid/solid/whatever then there's lot's of other stuff present and that alters how charges and their movements are 'felt'. So the permeability and permittivity are different depending upon the detail of that. Hence the speed of light is altered, which gives you refractive indices ( essentially a ratio of speeds ), Snell's Law and whatnot. You would deduce ( from the inverse square root of the product ) that since the speed of light is lower in materials than in a vacuum, then the permeability and permittivity are higher.
As regards a mass/energy equivalent to the field, then that depends. If the field is non-zero ( in the classical sense ) then yes you have an equivalent mass as you state. However in the modern view, one can talk of 'virtual' photons ( the field quanta ) that mediate interaction with charged particles. They are virtual because you didn't detect them. They'd be 'real' if you did. It's a throw/catch mechanism of a ball ( photon ) between two players ( particles ). So far so good.
But now you chuck in quantum, and Heisenberg, which allows 'short term debt' to/from the field. The more you take/give the shorter time you can do it for. Like a clerk who 'borrows' the bank's money for the afternoon to try his luck on a horse, you have to get it back in before reckoning by the day's close of business ( excepting that the horse falls at the first fence ). This inverts the idea of imprecision in energy/time resolution, by saying that anything can happen provided one stays under that resolution. So you have the presence of these virtual photons that no longer have the standard 'real' photon relationships for energy/momentum/frequency/wavenumber. So you don't have :
E = h * frequency
p = h * wavenumber
applying to these virtual guys. They are 'off mass shell', a reference to a particular graphical appearance of energy/momentum plots. The weirdo thing is if you do a sum-over-histories QM calculation for the wave functions, with contributions from all alternative mechanisms of interactions ( aka Feynman diagrams ) then you get the classical answers coming out. You get Snell's law and all of optics. It works. The permeability and permittivity are effective values based upon that deeper virtual mechanism. The more basic number here is the 'fine structure' constant that relates how strong is the EM interaction at a Feynman diagram nexus ( where lines meet ).
Now what properties of mass/energy do you attribute to the virtual particles? If anything can happen on a sufficiently short time scale then what is the mass effect of that? It turns out we needn't worry much, as with virtual particle creation & destruction we are talking about accounting in different areas. So the mass/energy of an electron/positron pair shifts from the 'electron' field to the 'photon' field when they annihilate to produce gammas. Like shifting money between accounts, credit card to savings, say. Conservation of energy says you don't lose money in the transfer, unlike real banks that charge a fee for the procedure! Anyone for a 'virtual' bank transaction? :-)
Coming to the end now! :-)
So there's energy in the vacuum, even if no-one is looking, or equivalently if no 'real' charges are about to be influenced. But all our calculations are indifferent to the choice of zero energy. We only ever measure differences between otherwise arbitrary levels. The 'virtual' vacuum energy can only mean something if we have another level where there is no vacuum, to then assess what the vacuum 'contains'. You can only talk of a glass full of beer if you have an empty one as an example. Can you compare The Universe with a vacuum to The Universe without the vacuum? Err ..... and this virtual particle energy, by definition, we cannot influence - if we did, they'd be real particles! So the definitions cover the accounting.
Alas this is the squirrelly ( certainly non-intuitive ) explanation that quantum mechanics forces us into. We add up things we can't actually sense, and never will, but the answers are so stunningly accurate. Whether you treat the virtual particles as 'legitimate' is a moot point. All science can say is that their presence in the calculation works as if they are present. Which is a bit of a circular argument, actually .....
There. Time for a lie down ....
Cheers, Mike.
( edit ) Hey, I've cracked 4M! :-)
( edit ) So comparing :
energy( vacuum + Chipper )
to
energy( vacuum )
only tells you something about Chipper. We want to see
energy()
but can't.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
Thanks, Mike. A deep well for sure – no problem with thirsting but 'my cup runneth over' faster than I can drink :))
To Wit:
Virtual particles aside for a moment, considering the photon energy density, note that the result is independent of spatial dimensions and can be applied to a region of space that's in equilibrium. Recall how the 'Ultraviolet Catastrophe' is avoided and note the comparison of curves showing the Rayleigh-Jeans Law vs. the quantum Planck Radiation Formula – comparing these to the equation for Newtonian gravitational force with the modified equation using the notion of 'separation threshold' (mentioned previously). Question: to avoid an infinite gravitational force (from quarks to black holes), what about multiplying the standard Newtonian equation by both the Bose-Einstein energy distribution function and the Fermi-Dirac energy distribution function ( i.e., 1 / [Ae^(2E/kT) – 1] )...?
RE: Well I suppose Matrix
)
Can't help thinking: There is too a Spoon!
Or does the sum total of the entire cosmos add up to nothing? -- even such an equation of state by itself is surely something!
Apologies if this is straying off-topic, can't help wondering if there is such a thing in physics :)
Have a gander at Null Coordinates, hopefully it's helpful ...
RE: Have a gander at Null
)
As far as I can penetrate the maths, it looks like a re-expression of known issues. He rotates the axes of measurement, essentially measuring spacetime events according to a photon's view. Obtaining the not-unusual result that the finite speed of light limits our knowledge of events, specifically matter outside the light cone cannot influence.
Just because one can derive an inverse relationship ( basically a faster moving object travels a greater distance in a shorter time ) doesn't imply 'uncertainty' in the Heisenberg sense. Actually I'm not real sure what he was getting at - specifically what new prediction/explanation would entail from the axis rotation.
This simply means that because the proper time for a photon is zero ( time doesn't pass at the speed of light ) implies that 'action at a distance' occurs. But the key point is missed : it doesn't matter what a photon experiences, as we're never going to ride one. The 'singularity' he describes is merely that one travels at the speed of light or one doesn't. And because you can't transition between the two ( you either have a rest mass or you don't ) then such viewpoints can never be compared experimentally. Although it might be great to hypothecate what might be an 'outside' view, this doesn't advance our understanding of entanglement.
I think he's confusing 'precision' with 'knowledge' here. If something is outside our lightcone it has neither a quantum mechanical value of 'expectation' ( average ) nor 'variance' ( spread about the average ) for us. Heisenberg is talking about variable pairs where mutual variance is constrained. Special relativity talks of whether you have an expectation at all.
An infinite speed of light would give you instantaneous knowledge, but that doesn't mean greater exactness. Quantum mechanical uncertainty doesn't flow from propagation delay. Or if it does, I can't see that his maths illustrates that. Stuff outside the light cone doesn't enter any prediction flowing from the wavefunction! To my knowledge no-one includes tachyons in sum-over-histories integrals. If you could do that, with a prediction that includes effects from said faster-than-light behaviour then you could measure experimentally against that.
Cheers, Mike.
( edit ) The ( special ) relativistic duality is that one can either increase the speed of a body in some frame, OR you can change the speed of the frame. You'll get equivalent descriptions with either, known as a 'Lorentz boost'. Whether this is observed by a sub-light speed observer or one at light speed makes no odds. In the sub-light frame/case you'll get a 'mass shell' curve for energy versus momentum ( where velocity is dE/dP and the energy axis intercept is the rest mass ) and the curves go asymptotically to the light cone. In the null co-ordinates instance you still get the same interpretation.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
Thanks Mike, these bits are
)
Thanks Mike, these bits are what caught my eye --
(emphasis added) and
and also the part right after that: “It follows that the scale factors of any two frames S_i and S_j are related according to
da_i = da_j * sqrt[(1+v_ij)/(1-v_ij)]
db_i = db_j * sqrt[(1-v_ij)/(1+v_ij)]
where v_ij is the usual velocity parameter (in units such that c=1) of the origin of S_j with respect to S_i.â€
(I understand what's meant by a Doppler shift, but not what it means to observe a 'relativistic Doppler shift', say as an up quark interacting with an up & a down quark as in the heart of a proton.) What especially caught my eye was that the terms with the velocity parameter are very close to the 'Gamma2' of this post which came from your idea of a 'separation threshold' and what that might mean for gravity below a certain scale ... so does it seem like there is a basis for the idea of a separation threshold that stems from (how to say it?) being mathematically undefinable or relativistically indeterminate, with regard to the scaling of singular null intervals in spacetime – that is, if the nature of matter is energy and the nature of energy is to be light-like? Am I comparing apples and oranges, or not even in the ballpark? (I know it's a ways from Dark Energy and GWs...)
And when the author remarked on not being able to perform precise measurements, my question was: Is quantum uncertainty and failure of simultaneity one and the same thing (mechanically), then?
RE: Thanks Mike, these bits
)
This simply means that special relativity doesn't predict a value for the speed of light - that is, the exact ratio between distance and time that photons travel. Special Relativity only says that light has a constant speed, not what that speed might be. You find that out by doing experiments and comparing light's behaviour with respect to your choice of standards ( meters & seconds say ). So if c did have some constant value other than the present one then the discussion remains the same, mutatis mutandis.
More of the same. In a universe with a different c value a null geodesic is still a null geodesic, but all the velocity dependent effects ( lengths & times ) vary as per the new choice of c. He is implicitly comparing two distinct universes, not relating measurements by different observers in the same universe. He's evidently confused 'frame' with 'universe', and hasn't grasped Special Relativity's principle that c is measured the same regardless of the choice of frame within the universe we inhabit. Specifically : the relativity he is discussing isn't the theory that was defined by Einstein. So he's talking about his own private understanding, or whatever. Which is OK. ( But you need to know that while you read him ).
I guess the problem with handling indeterminates is the following : it doesn't mean you can insert whatever you like, it means you can make no statement. One can misinterpret an old chestnut in logic :
Q. 'what follows from a false statement?'
A. 'anything'
But that means you have no basis to select any particular implication ( that follows from a false predicate ) over any other!
He seemed to be wanting to show that. I don't see that in what he has presented. Perhaps he might be trying to invent/state some sort of many-worlds hypothesis .... sort of the speed of light is different in some 'adjacent' universe from in ours, so that difference then causes what we perceive as quantum uncertainty in this universe? Who can say? :-)
On a semi-related note, I've seen a lecture by Roger Penrose where he discusses what to do at the 'end of the universe'. It would seem that pretty well everything would have decayed by then - protons, neutrons, all manner of exotica, black holes, white holes, wormholes .... except photons ( and maybe some electrons, which worries him ). How are any length/time scales defined? Or put another way, what gives quantum behaviour when there are no interactions? Photons are 'transparent' to one another and there certainly won't be any chance of converting them to even low mass particles. The second law of thermodynamics will have shaved all energy differentials to sweet stuff all ( well below the rest mass of anything ). A scale-less sea of photons ... so what exactly is space & time?
Cheers, Mike.
( edit ) I've re-read that thread you refer to. Fox News does indeed have warped branes ... :-)
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
Thanks for the prompt (and
)
Thanks for the prompt (and sharp-sighted) reply, Mike.
Yet it has one, very specific and finite, and out of all possible values it seems slow as molasses, practically zero compared to a number like Avogadro's constant, and the volume of a mole of anything is in turn practically nil compared to just the volume of the Earth... Confounding that the speed of light has to be a number that comes from somewhere/when/thing!
I understand what you say about the trouble with handling indeterminates, and appreciate the more proper perspective.
As for time, 14 billion years (about how long since the Big Bang) is practically nil compared to forever – a notion and amount of time that surely must've preceded everything ... ?
After this excursion I should really check to see if Fox News is hiring, feels like I'd fit right in! :))
I think that, in a sense, the
)
I think that, in a sense, the classical physicists were right about light. They had an aether which had some 'stiffness' on the one hand ( but was undetectable on the other ). The speed of light was a consequence of that stiffness, obviously by analogy with other wave phenomena. So tension/forces in a material would determine a speed of propagation. For instance loosely coupled particles, like air molecules, would have a certain velocity but strongly coupled atoms in a lattice of iron would be much higher ( speed of sound ).
But I don't think there is an aether. But I do think the speed of light would derivable from some more fundamental understanding of the universe. We call it the 'speed of light' basically because that's the way we have investigated and discovered it historically. In a hypothetical universe where Newton's constant G was much larger, and EM couplings much smaller, then we might be routinely talking of the 'speed of gravity' in everyday life but wondering about detecting electromagnetic waves at specially built detectors - "The Gaser Interferometer EM Wave Observatory" ?! Notwithstanding the question of whether we would exist in such a universe. :-)
So a speed for light would come naturally out of some deeper theory. I do wonder whether field theories are the way to go for that deeper dig. As they were prescribed to get around the 'problem' of action-at-a-distance, they can't really cope with QM entanglement.
It reminds me of a thing called a 'palimpsest', originally meaning a manuscript where the writing had been scraped off and the paper re-used by writing over again. Many of the old classic paintings had this, where there wasn't necessarily a removal attempt, and modern techniques can detect the image layer(s) underneath ( see the later production of The Thomas Crown Affair ). So what we perceive and are is the superficial layer of such a universe which is a palimpsest of sorts. Clearly this is the sort of area indulged in by the extra-dimensionalists like Lisa Randall. The deeper layers in the painting affect the superficial ones, and the trick will be to get a consistent understanding whereby a model of the underlying layer(s) yield observable effects. So entanglement might be explicable, say, and gravity's weakness is because of branes n' bulks n' stuff. Note that a Higg's detection wouldn't change this approach, Higg's is a way of expressing a vacuum property that leads to resistance to motion ie. inertial mass.
Cheers, Mike.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
RE: ....In a hypothetical
)
Wow ! In this universe, the Seti project “might†have some
actual scientific value.
Bill
RE: The speed of light was
)
I recall that the speed of light (c) is related to electric permittivity of free space (ε_0) and magnetic permeability of free space (μ_0) with the equation
c = 1 / sqrt(ε_0 * μ_0).
Can it be said that free space has a non-zero value of energy (E) that accompanies the electromagnetic field within it? Regarding a scale-less sea of photons in some near-point-like volume of free space (which said volume has light from all the stars and all the galaxies constantly and continually shining through it, not to mention the presence of a Dirac sea as well), would this not endow free space with an equivalent mass (m) given by
m = E * ε_0 * μ_0
( by substituting the first equation in the equation E = m * c^2 ) ?
Or if not free space then does the electromagnetic field by itself have that mass?
Ah, this is a deep well
)
Ah, this is a deep well indeed! Are you thirsty? One must be careful what one asks for ..... :-)
Yep, that's right. The permeability and permittivity ( while also having way too many syllables ) reflect the effect of static and time dependent charge distributions respectively. They are the constants of proportionality ( or derivable from same ) in Maxwell's equations. So they tell you how much force comes from how much charge and it's movement. If you take Coulomb's Law for a charge and apply the Lorentz transformation then you get two components. A static component that looks like Coulomb's and a velocity dependent part. Magnetism is the latter part, and is really the special relativistic effect of moving with respect to a charge. Or the charge with respect to you, same result either way. Interestingly the initial classical theoretical handling of the scenarios : observer moving, charge stationary vs. observer still, charge moving : were quite distinct explanations in detail, even though the answers yielded were the same in terms of what went where!
Or if you like magnetism is the force arising from where the charge was at some earlier time, accounting for the finite delay in force propagation ( at the speed of light ). So the faster you ( or the charge ) move the more lag you get because of the greater distance you travel in a given time. Sort of like a debt, you pay now or you pay later! You can run but you can't hide! :-)
[ Now the interesting thing that comes out is the direction of the relativistic/magnetic component. If you have two parallel current carrying wires they have a force between them. Not so if perpendicular. All those right-hand rules! ]
In free space, meaning when there is 'nothing' intervening between two charges those constants have a certain value. Within a given material, gas/liquid/solid/whatever then there's lot's of other stuff present and that alters how charges and their movements are 'felt'. So the permeability and permittivity are different depending upon the detail of that. Hence the speed of light is altered, which gives you refractive indices ( essentially a ratio of speeds ), Snell's Law and whatnot. You would deduce ( from the inverse square root of the product ) that since the speed of light is lower in materials than in a vacuum, then the permeability and permittivity are higher.
As regards a mass/energy equivalent to the field, then that depends. If the field is non-zero ( in the classical sense ) then yes you have an equivalent mass as you state. However in the modern view, one can talk of 'virtual' photons ( the field quanta ) that mediate interaction with charged particles. They are virtual because you didn't detect them. They'd be 'real' if you did. It's a throw/catch mechanism of a ball ( photon ) between two players ( particles ). So far so good.
But now you chuck in quantum, and Heisenberg, which allows 'short term debt' to/from the field. The more you take/give the shorter time you can do it for. Like a clerk who 'borrows' the bank's money for the afternoon to try his luck on a horse, you have to get it back in before reckoning by the day's close of business ( excepting that the horse falls at the first fence ). This inverts the idea of imprecision in energy/time resolution, by saying that anything can happen provided one stays under that resolution. So you have the presence of these virtual photons that no longer have the standard 'real' photon relationships for energy/momentum/frequency/wavenumber. So you don't have :
E = h * frequency
p = h * wavenumber
applying to these virtual guys. They are 'off mass shell', a reference to a particular graphical appearance of energy/momentum plots. The weirdo thing is if you do a sum-over-histories QM calculation for the wave functions, with contributions from all alternative mechanisms of interactions ( aka Feynman diagrams ) then you get the classical answers coming out. You get Snell's law and all of optics. It works. The permeability and permittivity are effective values based upon that deeper virtual mechanism. The more basic number here is the 'fine structure' constant that relates how strong is the EM interaction at a Feynman diagram nexus ( where lines meet ).
Now what properties of mass/energy do you attribute to the virtual particles? If anything can happen on a sufficiently short time scale then what is the mass effect of that? It turns out we needn't worry much, as with virtual particle creation & destruction we are talking about accounting in different areas. So the mass/energy of an electron/positron pair shifts from the 'electron' field to the 'photon' field when they annihilate to produce gammas. Like shifting money between accounts, credit card to savings, say. Conservation of energy says you don't lose money in the transfer, unlike real banks that charge a fee for the procedure! Anyone for a 'virtual' bank transaction? :-)
Coming to the end now! :-)
So there's energy in the vacuum, even if no-one is looking, or equivalently if no 'real' charges are about to be influenced. But all our calculations are indifferent to the choice of zero energy. We only ever measure differences between otherwise arbitrary levels. The 'virtual' vacuum energy can only mean something if we have another level where there is no vacuum, to then assess what the vacuum 'contains'. You can only talk of a glass full of beer if you have an empty one as an example. Can you compare The Universe with a vacuum to The Universe without the vacuum? Err ..... and this virtual particle energy, by definition, we cannot influence - if we did, they'd be real particles! So the definitions cover the accounting.
Alas this is the squirrelly ( certainly non-intuitive ) explanation that quantum mechanics forces us into. We add up things we can't actually sense, and never will, but the answers are so stunningly accurate. Whether you treat the virtual particles as 'legitimate' is a moot point. All science can say is that their presence in the calculation works as if they are present. Which is a bit of a circular argument, actually .....
There. Time for a lie down ....
Cheers, Mike.
( edit ) Hey, I've cracked 4M! :-)
( edit ) So comparing :
energy( vacuum + Chipper )
to
energy( vacuum )
only tells you something about Chipper. We want to see
energy()
but can't.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
Thanks, Mike. A deep well
)
Thanks, Mike. A deep well for sure – no problem with thirsting but 'my cup runneth over' faster than I can drink :))
To Wit:
Virtual particles aside for a moment, considering the photon energy density, note that the result is independent of spatial dimensions and can be applied to a region of space that's in equilibrium. Recall how the 'Ultraviolet Catastrophe' is avoided and note the comparison of curves showing the Rayleigh-Jeans Law vs. the quantum Planck Radiation Formula – comparing these to the equation for Newtonian gravitational force with the modified equation using the notion of 'separation threshold' (mentioned previously). Question: to avoid an infinite gravitational force (from quarks to black holes), what about multiplying the standard Newtonian equation by both the Bose-Einstein energy distribution function and the Fermi-Dirac energy distribution function ( i.e., 1 / [Ae^(2E/kT) – 1] )...?
edit - Congrats on cracking 4M, way to crunch! :)