Aethelwulf

So, it is hard to decide where this should be... quantum theory seems best but it may cover many topics. So, what problems face unification. I will be aware of many problems brought up, but I am interested in the different opinions by the posters here. I will post my own after a healthy dose of other contributions... trust me though, the problems are much vaster than those just lying with quantum gravity. Enjoy for now.

Sure, it is theoretically possible, since the vacuum is dynamic. Curving spacetime is enough to make distances shorten. This is the same idea, except in your case, you want it over large distances I'd expect.

Alcubierre drive (if I spelled that right) moves spacetime rather than the object in question, if that is what you have in mind. The drive itself is hypothetical but is allowable by physical laws. It could make an object move at or even over the speed of light.

I have a question... now this is based on memory, if I have anything wrong, please correct me... We have natural numbers, then it is imaginary numbers, then we work with quarternions, then it's... Octonians and then it is the Cayley numbers? Is that right? I hope there is nothing inbetween... ... anyway, I understand imaginary numbers and quarternions, I am a bit vague on Octonians and how many numbers they involve... but why does everything stop at the Cayley Number... is it something to do with the Division Ring?

Yes, energy and time are indeed measurements... However, the concept of observables puts into place a difference between energy and time... for instance; A good example of an observable would be spin. Even energy particles, like a photon has a spin which is a measurable property of particles. Time is not an observable in physics. So for this reason, I can agree that time is an invented concept. The word ''energy'' is also a concept we invented, but it surely was to describe ''a real thing'' .... whilst time is arguably something of more a book -keeping of events - like a clock measures a second pass, a clock is invented to measure that second pass. But energy is different, it has real physical effects on the world... whereas time is more like a coefficient to real events, if that makes sense at all? Again, time is not an observable, so I completely agree from this point of view.

The way you word this, forgive me for saying, sounds as delusional as a pre-industrial teacher.

If it is in an email, I should doubt it is in breach of copyright.

There are cases I might be able to come to agree on that energy is physically meaningless, like for instance, the self energy of an electron. [math]U_{e} = \int_{|\vec{r}| \leq R} \frac{\epsilon_0}{2}E^2 d\vec{r} = \int_{R}^{\infty} \frac{e^2}{8\pi \epsilon_0 r^2}dr[/math] When [math]R=0[/math] the energy of an electron is infinite. So basically all ''pointlike'' particles like electrons should have infinities energies - but they don't. This would be a case where the energy for me is defined as an ''unphysical case''. Of course, one way to solve this is by saying there is some kind of classical electron radius [math]r_0 = 2R[/math] but you say that normally to a scientist and they may call you a psuedoscientist. We should in my opinion, believe that there is an experimental limit on particles sizes, that below a certain threshold, whether a particle is pointlike or not, there will always be experiments which show they still act like pointlike particles, which is entirely conceivable. Back to the question of conservation for a universe, I don't quite know what you had in mind for the lack of conservation for a universe ''bringing in the meaning of energy'', but what I had in mind when you said this, I think of conserved quantities that are associated to the generators of the theory such as [math]UU^{\dagger} = (1 + i \epsilon T)(1 - i \epsilon T^{\dagger})[/math] which gives [math]i\epsilon(T-T^{\dagger})=0[/math] Where [math]T[/math] is the generator. This is of course is Noethers Theorem in a nutshell - a simple Noether Theorem example would be [math]q_i \rightarrow \phi_i + \epsilon f_i (q)[/math] Which is just a transformation with a small parameter in it, neglecting it we have [math]\sum_i P_i f_i (q)[/math] would be conserved if [math]\delta L = 0[/math] As I am sure you know, the system doesn't change, conserves it's quantity... but if this kind of idea does not work for the universe as a whole, perhaps we need to start defining our conservation laws into two distinct set of groups, the global case and the local case. Local Conservation works well, in the Global case it seems to break apart.... the question is why? Well we don't know, but perhaps there is a striking similarity to being unable to find a Global time. Indeed, to make a symmetry transformation on the energy of the universe, you'd need a Global time. Time in GR relativity vanishes completely http://en.wikipedia....DeWitt_equation and http://arxiv.org/pdf/0909.1861v1.pdf helps to explain the vanishing time derivative of the global wave function. Now, the meaning of energy for a global description may just be the same as the description of energy on local levels except for a small tweak, we might find for instance that energy is leaking from the universe which causes the non-conservational properties, or we might find that there is some kind of intrinsic link between the accelerated expansion of the universe and the non-conservation, or even both.

Are you trying to be obtuse? We have already agreed that it is inconsistent inasmuch that it cannot describe changing energy, taking into details like the loss of radiation. We've established this, and this is why I say it's inconsistent over periods of time. As has been noted, it is an approximation which works well. Now, it has also been noted that it's like dust off a golf ball, but I've argued that radiation may not be very smooth in this sense, we might be talking about an object which releases gamma energy in the form of jet bursts. Then surely in that kind of case, radiation will be given up a lot quicker. So I am not saying that it is inconsistent that we can't make approximations, I am saying it is inconsistent that it does not describe the energy given up over periods of time. This is why it cannot purport to a real object 100% accurately - it doesn't take into details of the energy given up through natural processes which would be expected from a metric. Now you have also said yourself that modifications are not unknown to the SC metric. This is exactly what my OP is attempting to do, but I need to find a way round the timelike killing vector, which won't be easy. Just highlighting this problem mathematically, the SC metric is invariant under the tranformation [math]t \rightarrow t+dt[/math] in the spherical coordinate system [math](t,r,\theta, \phi)[/math]. You split the vector field [math](dt,0,0,0)[/math] into two factors, the finite vector field [math]\Sigma[/math] and some infinitesimal scalar, then the displacement vector is [math]\zeta dt = (1,0,0,0) dt[/math] And this is the Killing vector. When all the points in the space are displaced they do not flow with any expansion or compression. And has been discussed, it contains a specific symmetry [math]t \rightarrow -t[/math]. I don't think my approach will be able to solve a way around the killing vector, its almost entwined in the definition of the SC metric... which means I need to look for a different modified approach.

Right... there is no one fundamental unit of energy.

Ok then, so back on topic. Do you think energy is physical? I think it's a bit of an oxymoron to say it isn't, since energy has real effects on the physical objects of the world, from everyday life to cosmology. I will be honest, I have never thought of energy as being ''unphysical'' until I came to this forum. When Swansont said, pour a glass of energy, the reason we can't is because it is not condensed like matter is, but is it wise to say it is not physical? If it is not physical what is energy, ethereal? Of course, this doesn't mean that photons are completely incapable of being described that way. I believe, in superconducters, photons behave as though they have a mass. So they certainly can behave like your normal everyday by changing the medium in which they are in, which is a clue they are not really unphysical manifestations.

Saying ''just the metric'' [math]g_{\mu \nu}[/math] is a massive oversimplification, but... your approach would be consistent when you proved [math]g_{\mu \nu} \ne 0[/math]. Anyway, I don't really think you are following my problems very well -- I am well aware of the Einstein Equations and the metric. This is not what I am talking about. I was concerned strictly with the SC metric would does have inconsistencies. Elfmotat had the right suggestion for me http://en.wikipedia.org/wiki/Vaidya_metric I'm wondering now if Hawking radiation would account for loss of radiation in a non-rotating black hole, but since the Schwartzschild metric is static and t-symmetric, I am wondering if Hawking's work has been able to solve equations for a static black hole. If one cannot do it in any way, I'd dare say the Schwartzschild metric does not really purport to a real type of object.

So does mass however, mass has many forms. I don't know if saying it has many forms can preclude that energy is not physical. I could try and find some and I certainly have my own idea's for sure... I don't know if posting them here in this subforum would be within the rules... One quick one however, the fact that the observable universe is now receding faster than light is an indication that the universe is using energy at a rapid and accelerated rate. This may be an indication that the universe is not conserving energy. I believe the universe might quantum leap in the future. Current mainstream seems to agree with the prediction of my own http://www.scientificamerican.com/article.cfm?id=is-the-universe-leaking-energy As wiki explains ''In general relativity conservation of energy-momentum is expressed with the aid of a stress-energy-momentum pseudotensor. The theory of general relativity leaves open the question of whether there is a conservation of energy for the entire universe.'' http://en.wikipedia.org/wiki/Conservation_of_energy

Thank you, never heard of it... a new subject for me to learn the next few days. One difference though is that it is not static.

I'm quite sure that is meaningful, but if it was it went right over my head Swansont. Ok... I guess the most logical question is, why can't you generalize to photon energy? When you say energy, what kind of energy did you have in mind? I have good faith in them. I like it. I like the idea that a universe does not conserve energy, globally-speaking.

I see what your saying, I do... but I feel the word ''unphysical'' is quite a drastic use of the word. Should ''unphysical'' be the word we use? Hands up I don't know. I just think it would be hard to say energy is not when it has real effects on the physical world. Now, sure we cannot pour a cup of energy. There are some models which treat photon energy however as a gas - with a temperature, pressure and entropy. Black body radiation is said to be the equilibrium of the photon gas... and we don't think of gas as unphysical do we? I don't know.... ''unphysical'' to me, just seems like something which shouldn't effect the physical world, but energy does so... Hello pmb, I read your work, it is a good read for anyone who is wanting to learn this stuff... I perhaps only have one suggestion - it's a bit of a quibble. ''Notice how the energy moves back and forth from system to system yet the total energy of the universe remains constant. '' I don't think current mainstream cosmology believes that the universe conserves energy any more. (Here's a paper which entertains the idea that the zero point energy field is a physical manifestation http://arxiv.org/abs/hep-th/9901011 ---- I think the problem here will lye in how to persuade people to think of energy as a non-physical entity. I gave some reasons above. I could be completely wrong and you two could be completely right, certainly wouldn't be the first time I have been wrong.)

Here I will assume by simple, we really really mean a first approximation in energy - and higher perturbations could not be calculated because the metric is static - though the metric surely would change over time, so it seems the SC is an oversimplification of the real dynamics going therefore the problem lies within the consistency over long periods of time. How accurate would it be for a system which was radiating fast, perhaps in some kind of plasma-like bursts? Given enough time, I'd say it was pretty inaccurate; which leads me to my own question, is there any non-rotating metrics out there which can describe systems more accurately than a SC metric? I don't believe there is. Sure, but these things aren't being question. All I am questioning is how a metric like this can remain effectively at the same energy level over short or long periods of times. Even after long periods of time, the SC metric becomes inaccurate in explaining your system because no doubt in many cases, the system will have given up energy in the form of radiation. My studies right now is trying to find a way round that problem - I guess it doesn't help that the Schwartzschild metric is derives from principles which require a timelike killing vector making it essentially static and t-symmetric.

Yes, it's not the gravitational field per se, but the Higgs Field is composed of Higgs Bosons which get their own mass from it's own field as well. So not only do other particles acquire mass from the Higgs Field, the Higgs Field gives a mass to its own particle... So.. since these Bosons contain a mass, then this means they interact gravitationally as well. Yes, I would presume they are the same by the Weak Equivalence principle - here we freely exchange the use of ''inertia'' and ''gravitational mass''. I do believe I read an article by Wheeler who was saying that the treatment of mass as a charge would not be so strange - I have never found this article since mind you.

Well, it's not exactly unphysical in the eyes of General Relativity. What is unphysical about energy, which can warp the spacetime fabric? Curvature is the storage of energy in the spacetime metric, how can one really call it an unphysical manifestation? Can I read your work later, btw, I need to go do something the now. Thanks.

Uncertainty for me, is the lack of knowledge from an observer. Of course, the most basic explanation is that it requires two complimentary observables which are of course conjugate quantities, such as energy and time or momentum and position. However it holds a type of mysticism for me because it is the inability to predict the future based on the present - which means that ordered sets of events are hard to determine.

Hmmm.... ... I disagree with energy not being a physical ''thing''.... The rest I agree with. Physical is not restrained to mass. The conjugate of time, but even in relativity time is considered physical in that sense of the word. For instance, in General Relativity, space is not separate to time. They are the manifold we treat as being a physical sheet.

Special Relativity is easier to understand the the General case... I can help with both, not just explanations, but mathematically I can explain it too... but it won't be easy without a mathematical background...

Can I ask what it is meant to be then? thank you.

The reasons why there is no center have been explained here by many. It has to do with the fact that the universe is expanding isotropically and homogeneously. There can be some kind of ''imaginary center'' we all think about, a place or rather a point where spacetime began, but thinking of that point after the expansion is useless when you take into account that all objects move away from each other, not from a single point.

It's doubtful you can have a universe in another universe if they are exact copies. No subsystem can precisely model the larger system it is made of. Nor do I believe that parallel universes exist because there should or cannot be any system isomorphic to the universe.