Aethelwulf

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Posts posted by Aethelwulf


How do you propose bypassing the Coloumb Barrier at low temperatures?
Who me?
Such as would be found in the proton cycle in stars, such a barrier is penetrated by tunneling effects allowing the process to occur at much lower temperatures.
So not all cases actually require extremely high thermodynamical transition phases.
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The results from this year are actually just confirmation that they found it last year.
''Think'' they found it and none of the results are conclusive. It will need more tests.
http://www.guardian.co.uk/science/2011/dec/13/higgsbosonglimpsedcernscientists
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Well, let's not all be too harsh. Some scientists have seen merit in it. Schwinger, perhaps one of the most prominent scientists of all time wrote eight papers on the subjects.
There is of course no reason to think it is not possible. To date, it has drawn a lot of attention, on and off.
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Now, just as Motz had made clear in his paper, the Schwinger Quantization method for charged particles in fields takes on a remarkable similarity to the gravitational charge [math]Gm^2 = \hbar c[/math]. The link here will explain the charge condition:
http://encyclopedia2.thefreedictionary.com/DiracZwanzigerSchwinger+quantization+condition
What we essentially have is
[math]\frac{e\mu}{c} = \frac{1}{2}n\hbar[/math]
The gravitational charge quantization is
[math]\frac{Gm^2}{c}= \hbar[/math]
So motz was absolutely correct in stating the importance between the two equations.
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Quantum tends to be as ''elementary'' as you can get for any particle. There is such a thing as a quantum number for photons, called their spin states.
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I added to my post to get that equation into a form you might find more familiar. And yes, H is the Hamiltonian.
Following my own example, I end up with
[math]i \hbar (\frac{\partial \phi(t)}{\partial t}) = \lambda \phi(t)[/math]
The left hand side is the energy operator
[math]\hat{E} \phi(t) = i \hbar \frac{\partial}{\partial t} \phi(t) = \lambda \phi(t)[/math]
Does the fact you end up (in your simple method) using a force operator make my method wrong?
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So you are using capital P as a symbol for momentum  didn't know that one, I always think of that as pressure. And why are you introducing springs into Newtons second law?
And in your second equation you still seem to have change of position and time on the LHS and the unusual spring resorative force on the RHS  but where has the mass (relativistic or not) gone?
There's nothing mystical behind the use of Hookes law here. Just looking at my notes, it's just the way I defined the force. All your relativistic dynamics are still wrapped up in the [math]dp/dt[/math] (used a little p now to halt any confusion).
Yes, Equation two should be written like that. The first term [math]i\hbar \frac{\partial}{\partial x}[/math], do you recognize it? It's the momentum operator, we get this when we quantize the equation. That means what we really have [math]\frac{\partial \hat{p}}{\partial t}[/math]. This is why there is a mixture of the change in position and time on the LHS like you spotted.
I don't get it, why don't you just use [math]F=\frac{\partial H}{\partial x}[/math]? You could take the gradient of the Schrodinger equation to get: [math]i\hbar \frac{\partial }{\partial t}\nabla\Psi=\hat{F}\Psi [/math].
This is all very messy and unnecessary by the way.
What's H? Anyway, assuming your approach is correct, that's fine and all dandy. But I wanted to specifically quantize the second law.
Ah H is meant to be the Hamiltonian yes?
Should it be defined as a Hamiltonian, I thought W=Fx?
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I'm sure Hawking did not say we could exist outside the universe or see anything before the beginning of time itself.
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It was already commented before that one cannot universally claim that eA is a fieldlike momentum. since you insist on repeating the claim I will add more info.
If one restricts himself to field electrodynamics, sure that eA is related to the field, but when one works with WheelerFeynman electrodynamics or with more advanced and recent formulations of electrodynamics the term eA is not related to any field because A is given as a functional of particles path.
In the first place, the geodesic equation of motion does not includes partial derivative but total ones [math]d/ds[/math].
In the second place, [math]s[/math] in the geodesic equation of motion cannot be proper time for massless particles.
In the third place, pmb's [math]v^i[/math] cannot be derivative with respect to s, unless he is now using another notation than that he used before here when he tried to define kinetic momentum (e.g. in #3).
In the fourth place, [math]m\Gamma_{ij}^{k}v^i v^j[/math] is not a gravitational force because it includes a Christoffel symbol! Gravitation is not a force in general relativity.
Well, his paper defined it as the gravitational 3force. Don't shoot the messenger, this is why I asked the questions I did.
I would say, should it be surprising that a force can have a christoffel symbol in it? I mean... after all, the Christoffel Symbol (is the gravitational field) in GR.
(more) I have the geodesic equation written down somewhere, I was working by memory... but if you say so. The equation however will not describe massless particles, since the equation has M defined as a gravitational charge, or passive mass in other words. So yes, s would be the proper time interval.
Here it is. You where right, it is not partial derivatives, but it does use proper time.
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From F=ma and a²+b²=c² we unambigiously conclude that [math] F = m \sqrt{b^2  c^2} [/math]. Since we are in a relativistic framework, we know that E=mc². Therefore, [math] F^2 = m^2 b^2  mE [/math].
That doesn't make any sense to me.
I take it that was an attempt of a joke.
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Youve lost me at the first line  I still think of N 2 Law as f=ma! Could you explain your symbols and assumptions so the members can keep up.
[math]F=Ma[/math] is not true in relativity. The force equation which remains unchanged in relativity is
[math]F=d(m_{rel}v)/dt[/math]
The reason why is because in [math]F=Ma[/math], mass is generally a constant which is not true in relativity. I had a little look on line and there is a wiki article which mentions it:
http://en.wikipedia.org/wiki/Mass_in_special_relativity
Oh, and kx is just hookes law for force.
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I decided to quantize Newtons 2nd Law
[math]kx = \frac{\partial P}{\partial t}[/math]
today. Has anyone done this before? I need some help.
I start with quantizing the equation, naturally;
[math]i \hbar \frac{\partial}{\partial x} (\frac{\partial}{\partial t}) = kx[/math]
Hitting it with a wave function [math]\Psi = \psi(x)\phi(t)[/math] gives
[math]i \hbar \frac{\partial}{\partial x} (\frac{\partial \phi(t)}{\partial t}\psi(x)) = kx \psi(x)\phi(t)[/math]
To solve it we are therefore going to use the separation of variables method. (But I need you guys to make sure I am doing this right)
Divide through by [math]\Psi[/math] gives
[math]i \hbar \frac{\partial}{\partial x} (\frac{\partial \phi(t)}{\partial t}\frac{1}{\phi(t)}) = kx[/math]
So this is as far as I have got. Should I move the [math]\frac{\partial}{\partial x}[/math] term to the right as
[math]i \hbar (\frac{\partial \phi(t)}{\partial t}\frac{1}{\phi(t)}) = \frac{kx}{(\frac{\partial}{\partial x})}[/math]
So that on the left I purely have variables of t and on the right variables of x?
I think this would mean that both sides are independent, meaning that they equal a constant?
[math]i \hbar (\frac{\partial \phi(t)}{\partial t}\frac{1}{\phi(t)}) = \lambda[/math]
[math]\frac{kx}{(\frac{\partial}{\partial x})} = \lambda[/math]
Then I would like to concentrate on the timedependant case
[math]i \hbar (\frac{\partial \phi(t)}{\partial t}) = \lambda \phi(t)[/math]
Will now be
[math](\frac{\partial \phi(t)}{\phi(t)}) = \frac{i\lambda}{\hbar}\partial t[/math]
[math]\int (\frac{\partial \phi(t)}{\phi(t)}) = \int \frac{i\lambda}{\hbar}\partial t \rightarrow \frac{i\lambda}{\hbar} t +C[/math]
Then the solution would be [math]C e^{\frac{i \mathcal{A}}{\hbar}}[/math] where I have let [math]\lambda t = \mathcal{A}[/math].
Does this seem right, or have I messed up somewhere?
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I thought you were replying to me.
I apologize.
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I am not aware of any interpretation that states the length contraction is an illusion and time dilation is real or viceversa. And ACG52's point about conspiracy is welltaken. That's a selfadministered dose of Hemlock.
I never said it was an illusion. You need to start reading more carefully Swansont. You have a record with me now of not reading people correctly.
I said time was not a physical phenomenon.
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Pmb, where was the thread you posted your work on mass? Was it this one, I had been looking for it because I had a question.
In your paper, you define the gravitational charge component in a gravitational 3force equation. I believe it had the form
[math]f^k = m\Gamma_{ij}^{k}v^i v^j[/math]
I just wanted to know, how one would derive this equation. Presumably the connection is playing your usual role of the gravitational field yes? I see there is a dependance on the velocity. The [math]\Gamma_{ij}^{k}v^i v^j[/math] part looks a little bit like it comes from the geodesic equation of motion which involves usually a term of second derivatives.
The equation I had in mind was this one
[math]\frac{\partial^2 x^{\mu}}{\partial s^2} + \Gamma^{\mu}_{ij} \frac{\partial x^i}{\partial s} \frac{\partial x^j}{\partial s}=0[/math]
Ok, they look quite different but if you rearrange it
[math] \Gamma^{\mu}_{ij} \frac{\partial x^i}{\partial s} \frac{\partial x^j}{\partial s} = \frac{\partial^2 x^{\mu}}{\partial s^2}[/math]
The left hand side of the equation does look a little like
[math]\Gamma_{ij}^{k}v^i v^j[/math]
So I am just wondering how the force equation ''gets'' the terms it has. I'm especially interested in the dependence of the velocity and how this comes about.
Pmb, where was the thread you posted your work on mass? Was it this one, I had been looking for it because I had a question.
In your paper, you define the gravitational charge component in a gravitational 3force equation. I believe it had the form
[math]f^k = \Gamma_{ij}^{k}v^i v^j[/math]
I just wanted to know, how one would derive this equation. Presumably the connection is playing your usual role of the gravitational field yes? I see there is a dependance on the velocity. The [math]\Gamma_{ij}^{k}v^i v^j[/math] part looks a little bit like it comes from the geodesic equation of motion which involves usually a term of second derivatives.
The equation I had in mind was this one
[math]\frac{\partial^2 x^{\mu}}{\partial s^2} + \Gamma^{\mu}_{ij} \frac{\partial x^i}{\partial s} \frac{\partial x^j}{\partial s}=0[/math]
Ok, they look quite different but if you rearrange it
[math] \Gamma^{\mu}_{ij} \frac{\partial x^i}{\partial s} \frac{\partial x^j}{\partial s} = \frac{\partial^2 x^{\mu}}{\partial s^2}[/math]
The left hand side of the equation does look a little like
[math]\Gamma_{ij}^{k}v^i v^j[/math]
So I am just wondering how the force equation ''gets'' the terms it has. I'm especially interested in the dependence of the velocity and how this comes about.
I'm actually starting to think its definitely from the geodesic equation. The s is just 'proper time'. ct = x and c = x/t.
[math] \Gamma^{\mu}_{ij} \frac{\partial x^i}{\partial s} \frac{\partial x^j}{\partial s} = \Gamma^{\mu}_{ij} v^i v^j[/math]
I think that works out.
This adds up to the same dimensions as you find in that force equation. But then I start thinking about the dimensions of the equation. [math]m\Gamma^{\mu}_{ij} v^i v^j[/math] How does this equate to a 3force? If we just take it at face value, the part described as
[math]\Gamma^{\mu}_{ij} v^i v^j[/math]
would have to have dimensions of acceleration.
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Although Einstein used an explicit operational approach in his Special Theory, he was unable to use a mathematical approach that encapsulates his operational definitions since the actual mathematics was not discovered until 1961. Einstein and Hilbert used what was available to them at the time. Further, I respectfully submit that one of the greatest absurdities within modern science is that the concept of "time" is altered by physical behavior or physical entities as if "time" itself is a particle or field entity or the like.
I read everything, but this part struck me the most.
I agree it was an absurdity, but I think it came about because of the unification of space with time. I think, because fields could create a gravitational distortion in space, then time somehow was physical. Which is a load of rubbish. I think today, time is one of the most misunderstood concept there is  and a much abused one, where people often I read equate motion with change and a change with time, or that time is something which can be observed because there is a clock on the wall... these things are just ridiculous. Time does not mean change nor is time an observable, just as much time is not a real physical entity.
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I've recently been listening to some talks by Peter Atkins, a chemist and popular science writer, and I've heard him a couple of times talk about the beginning of the universe in terms of "nothing coming from nothing." This is because he says that current data in cosmology tentatively indicates that the universe might have a total energy of 0, and, therefore, the universe ought not be considered to be something coming from nothing, but nothing separating into its component, selfannihilating parts.
Is there a name for this theory in physics? Does it have many proponents? Can anyone elaborate on it for me?
Yes, it is called the Null Energy Condition.
[math]Mc^2  \frac{GM^2}{2R} = E[/math]
When [math]M=0[/math] it is said you are left with the metric.
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Can you explain to me, in your own words, the reason for a gravitional 3force. I see it in your paper, but you define mass as the gravitational charge  this is not the same kind of charge I think of or another author... can you elaborate on your christoffel symbol and its use, thank you.
Regards.
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Well, no one moved my post; It seems outside those who can answer it. I want to know what the speculators say.
Speculate away.
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While on a train today, I came to a question I could not answer. It grew from recent talks on the WheelerdeWitt (WDW) equation ... whilst I have pretty much advocated the idea over many years that we may actually live in a timeless universe (as many scientists have), it did cross my mind to believe that perhaps I have had it all wrong and that I must at least entertain the idea that the WDEequation has it all wrong. I considered some reasons why this approach could be wrong and I came across a question I couldn't answer within myself.
The WDWequation is obtained from quantizing the Einstein Field Equations  the general relativistic equations which describe curvature in the universe  noting this in my mind, I reminded myself that the wave function of the WDWequation was a global case, describing the entire universe. However, I have known for a while that the Wilkinson Microwave Anisotropy Probe has determined that we live in a universe which is more or less flat, which begs to question whether General Relativity would effectively break down on large enough levels.
If the universe is flat therefore, it seems unreasonable to attend idea's about it from equations which satisfy curvature [math]g_{\mu \nu} \ne 0[/math]. Instead it seems only reasonable to use the Newtonian Limit
[math]E = \int_v T^{00} dV[/math]
The WDWequation is derived from the equations which describe curvature, but if this is not the true configuration of the universe at large, then we might assume that many of the problems which have arisen from the WDWequation, such as a timelessness and even the noncomplexifying wave function (real) have arisen from faulty premises to begin with. Instead, should we not be trying to quantize an approach which actually fits the universe at large, one that is pretty much flat in all directions we look?
(On a separate note)
It also occurred to me that the universe would appear mostly flat if it was rotating (So in its natural form, it would be sphere like, if it was rotating, it would be flatdisk like). But that's for another discussion.
Is this thread a matter of no one can, or no one will answer it?
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The Chaldeans had in fact placed a lot of numerical significance to words.
This does not prove the case of the OP however.
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You don't see the contradiction between the statements. You can't get smaller than a photon, and yet a photon does not have a fixed size. A photon can be smaller than another photon which is the smallest. You can present a photon, the smallest piece of energy, and yet I can present another photon that's smaller. Makes "smallest" kinda meaningless, doesn't it?
Yes, of course I realize that, which is why I said you need to adjust the frequency as I said. When you do, no particle of energy can adjust to ''its'' size. We are talking about a very simple photon.
All particles have sizes, but without the splitting of hairs, the photon can be the smallest and is the smallest.
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You also misread the Wiki article, which shows that it is not my fault.
Quite possibly so.
I emphasized in my previous message #14 (which you read and replied) that the SS equation is more fundamental and general than the WdW equation. I did also explicit that the SS equation is "defined in a generalized Hilbert space beyond the scope of the WdW"... Evidently your above question is nonsensical.
Bolded by me.
How so?
Also you make a point saying the SS equation is defined in a Hilbert Space beyond the scope of the WDW equation. It is true the wave function of the WDW equation is no longer a spatial function, however, the operator H is a relativistic case which does act on the Hilbert Space.
You've made no comments on the complexifying of the SS equation, or the deep phyiscal meaning I purported to when physicists view quantum gravity under the noncomplex wave function.
( I realize in post 14 I said the time dependant SE is the analogue of the WDW equation  this is a mistake, I meant the time independEnt case).
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A basic introduction is given at http://en.wikipedia....vistic_dynamics. Therein "coordinate time" is the x^{0} and the "invariant evolution parameter" or "parametrized time" is [math]\tau[/math]. This fundamental time [math]\tau[/math] is defined globally, for the universe as a whole, and it coincides with the quantum mechanical concept of time.
Wheeler and DeWitt confounded the "t" in quantum mechanics with the "t" in general relativity and developed the nonsensical WdW equation, which leads to nonsensical claims about a timeless universe...
I have been reading more on this subject and I am not convinced that this is a viable approach for quantum theory in its treatment of gravitational physics. The Hamiltonian and momentum contraints of General Relativity yield the socalled ''nonesensical'' idea's you refer to, the timeless scenarios. However, many physicists feel there is a deep meaning to this, and is rooted much deeper than timeless equations like the time dependant Schrodinger Equation which is the analogue equation of the WDW equation. The reason why is because not only does time vanish but also complexification. The WDW is inherently real and if this approach is true it has massive implications for quantum gravity (many of them I bet are overlooked by scientists today).
I'd like to see a more rigorous reason for a time parameter/ evolution parameter or whatever name you wish to dub [math]\tau[/math] (Personally I prefer a Parameterized Time.) . How do you derive the equation above from the WDWequation? Notice that your complexification in the StueckelbergSchrödinger equation is achieved by making mention of time again in your universe. Why should we take it seriously rather than the WDW equation which has been derived from as one might see it, General relativistic first principles? I have read that this evolution parameter may have physical measurable properties. A bizarre statement if [math]t \rightarrow \tau[/math], since [math]t[/math] is not an observable  then it made talk of designing evolution parameter clocks... which is just another clock on the wall? This doesn't mean you can ''observe time''. I blame the wiki article for bad use of language. I have noticed one thing  it all heavily relies on the so called, ''reversibility of time''. Since it is a much abused concept, I am not convinced by this approach one bit  I also notice that the wiki article tries to justify reversibility by noting that antiparticles in a Feynman Diagram appear to move back in time.
No selfserving scientist actually believes this though.
I'd also like to note that whether you think it is nonsensical or not, timelessness is a growing phenomenon that is being appreciated by more and more physicists. I don't find it nonsensical. I think what is nonsensical is to believe time exists outside of the mind, objectively and independently of a recording device.
I notice also in the WIKI article, it says as a hypothesis:
''Hypothesis I
Assume t = Einsteinian time and reject Newtonian time.''
What's hypothetical about this? This is what has happened. Einsteinian time overthrew Newtonian time a while back now. Newtonian time consisted of absolute clocks in the universe  he also perceived time as something which inexorably flowed from past to future. Both these concepts have been shown to be the wrong kind of view of time, so I don't understand why this all stands on ''hypothesis 1'', also, even if one considers the coordinate time, it's use is really only valid for local events. Einstein showed that whilst you can view time as a component of the metric, his general relativity was in essence rooted from timeless propositions, world lines which where static for instance.
Interestingly, there is not even a past or future in relativity. In physics today most of us come to realize all you can really talk about is a present moment which is unceasing. That's perhaps the most solid kind of time you may ever be able to talk about.
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Coldfusion?
in Speculations
Posted
Well, I gave a demonstration that it can actually occur at lower temperatures using a tunneling processes. Certain stars work this way.
For a more conventional answer, I don't have one, but we should keep our minds open for we do not know all the processes behind nature. Remarkable breakthroughs of similar nature by unlocking the secrets of the fundamental universe have been made in such ways.
I'm a bit rusty on Schwingers work now, but he did work on latices for cold fusion http://www.infiniteenergy.com/iemagazine/issue1/colfusthe.html