joigus

Oh it doesn't work on so many levels... What about starting with animals generally died in the strata where they lived. Plus T-Rex is one of the most abundant fossils out there. Swamps and marshes leave abundant organic residues easy to recognise. Not the case. Unlikely... unless they all went en masse to Utah to embrace Mormonism in a retroactive mass conversion.

The unbalance cannot come from random fluctuations. Electric charge is exactly conserved --as every other gauge charge. You really need a mechanism to nudge things out of balance. Look up Sakharov conditions for baryogenesis. Oh, look. I thought I'd said it, and indeed I did... This is no random fluctuation. Either that or everything started out unbalanced for some mysterious reason --which is always possible.

That is so passé. History always almost repeats itself, but not quite.

Mind you, the site will be down (for the same reason) in about 2 years time now. A genie told me. So brace yourselves again for the temporary disappearance of your science-minded online persona in 6.2x107 seconds.

Not me. I had completely forgotten about this conversation! This feels like a dream... Did I really say that?

Liver I think symmetry and simple patterns are part of the deal. That would be my guess anyway. I understand we're just guessing...

Reported. I'm done with this.

I have read it --well... skimmed through it, obviously. I haven't seen any calculations of the properties of the vacuum. Not even back-of-the-envelop calculations. So I'm actually not engaging in any proper discussion of your theory because I don't see anything worth discussing. I'm just pointing out to you what I see as obvious deficiencies in your reasoning, so it's more of a rebuttal than a discussion. https://www.scienceforums.net/guidelines/ Point 7 of the Guidelines at SFN: So no, I do not have to read your document in any degree of thoroughness. Copy and paste anything from your text if you think it addresses any of my concerns. That'll do. Matter goes through the horizon, and we have strong reasons to believe thermal radiation slowly leaks out of it. I don't think your claim is consistent with Liouville's theorem, and probably many other principles of physics. It would only work in two isolated universes: One only with positive energies and time going in one direction; and another with the situation reversed. Nothing from one "universe" touches anything from the other, so there's no conflict in your mind. In your mind there is no conflict because it's all taking place in your mind. In the real world, No, you haven't deployed any convincing argument that your picture is consistent, and you have shown basic misunderstanding of the connection between symmetries and conservation laws, misunderstanding of the difference between passive transformations (sheer re-labelings of coordinates) and active ones (actual changes on the system) etc. And, as I told you, you've been here before with what appears to be the same crazy idea: https://www.scienceforums.net/search/?q=muruep&quick=1&type=core_members

No, that's no what I'm asking. Again: Which was in answer to: (My emphasis.) The vacuum being stable or not is one thing. Signals, electromagnetic or otherwise (meaning radiation, not the interactions themselves) leaving the horizon of a BH is a completely different matter. (I see now though that you have chosen to completely ignore Hawking radiation as a possibility.) You haven't proven that the vacuum under your scenario is stable or, I don't know, could lead to a runaway process near the horizon, or an explosion into gamma rays, or rotating cups of tea, or... You see? You haven't proven anything (or shown a robust argument using reliable principles of physics) why what you say should be right. You hope the vacuum would be stable under your scenario. That much is clear to me. But, as they say, hope is not a strategy.

Ok. The only thing I'd say is that it's not unique. As to the sequence of 0s & 1s actually representing the expansion of the ordering in base 2, I had never noticed. I suppose that's why people in quantum computing chose that convention for the product. It's nice to know. And... wow! You're on a QC binge!

I understand they're asking for a projector that embodies this measurement. You should not use a difference of projectors, as a difference of projectors is not a projector, even though the addition of two mutuallly orthogonal projectors is: \[ \left(P+P^{\perp}\right)^{2}=P^{2}+\left(P^{\perp}\right)^{2}+PP^{\perp}+P^{\perp}P=P+P^{\perp} \] But, \[ \left(P-P^{\perp}\right)^{2}=P^{2}+\left(P^{\perp}\right)^{2}+PP^{\perp}+P^{\perp}P=P+P^{\perp} \] But the operator you've written does commute with both \( P \) and \( P^{\perp} \), so it could implement such measurement, IMO. People who work in QC are very old-school though, so I assume, for them, nothing but a projector will do. Also, I don't remember the ordering of the computational basis. Clearly, \[ \left|0\right\rangle :=\left|000\right\rangle \] and, \[ \left|7\right\rangle :=\left|111\right\rangle \] But the rest I forget. Sorry, there should be a couple of minus signs in the last equality, but it doesn't matter, as they are mutually orthogonal. That's why I was sloppy.

Exactly. As you see, Dirac's notation can handle it by using extra round braces. But it kind of becomes more awkward --or perhaps just uglier-- for those cases. And it's a huge inconvenience when you want to talk about time inversion operation, because it's not even linear, but antilinear, so it has a complex conjugation in its guts that "interferes" with the complex conjugation involved in passing from ket to bra.

Yes. On the one hand stating more clearly that what you're saying is that every \( \left| q \right\rangle) \) in the space can be written as \( \left| v \right\rangle + \left| v_{\perp} \right\rangle \) (what I've written as \( v=v_{\parallel}+v_{\perp} \) ), and on the other hand, noticing that taking the action of \( P \) from the second to the first factor in the scalar product is not simply "looking at it as acting on its left", but also complex conjugating. In matrix notation: q⁺Pr=(P⁺q)⁺r where "+" as a superindex means complex conjugate and transpose. It's only when P⁺=P that you can write, q⁺P=(P⁺q)⁺=(Pq)⁺ Otherwise, you can just say that q⁺P=(P⁺q)⁺, which is always true, because it's a definition. This you cannot say clearly in Dirac notation, as Dirac notation automatically assumes that any operator "sandwiched" between both factors is Hermitian. Otherwise the notation is ambiguous. That's why someone as careful as Weinberg sometimes drops it in his proofs. Weinberg proved most everything he said, so he was very careful about these questions. The point of the exercise being that the eigenvalues of any projector are always real. Something that is not true for any linear operator. Another way of seeing it is by investigating the eigenvalue equation. As P²=P, the eigenvalues must satisfy p²=p, so either p=0 or 1.

You're most welcome. The rest of the expansions seem right to me. As to proof 4.3, I see what you're doing there, and it's correct too, AFAICS. The only glitch is for these kind of proofs is that it's perhaps best to drop Dirac's notation, because it kind of stands in the way of distinguishing the vector, the operator, and the action of the inner product more clearly, so you wouldn't have to use the --somewhat awkward, IMO-- double parenthesis on your last line. So, for example, I would write something like, for every \( w \), \( v \) in \( \mathscr{H} \) (the Hilbert space of states), \[ \left( w, P\right) = \left( P^{\dagger}w,v \right) \] (That is just a definition of \( P^{\dagger} \), of course) I would also write, \[ v=v_{perp}+v_{parallel} \] etc, with, \[ Pv_{perp}=0 \] \[ Pv_{parallel}=v_{parallel} \] for an arbitrary vector \( v \). And then, as you say, \[ \left( w, Pv \right) = \left( w,w_{\parallel} \right) = \left( w_{\parallel}, v_{\parallel} \right) = \left( w_{\parallel}, v \right) = \left( Pw, v \right) \] So indeed \( P^{\dagger}=P. To me, it's a bit more transparent with this notation, but I understood what you meant, and if you think about it we're saying the same thing. The devil is in the details, as they say. In infinite dimension one would have to be much more careful than this, but I don't have the chops for it. 😊 Ok. Something got messed up in the LaTeX rendering, I'm afraid... I hope you can see what it is. I always have to be very careful that my text is not interpreted as rich text at some point (eg, when the editor refreshes) so the rendering is messed up. It might have to do with the software at my end. I dunno.

Give me some time to check conventions. They differ from QC to "atoms-and-molecules" QM... But arent you missing 1/sqrt(2) factors there? Plus and minus kets should be normalised. Didn't get the time to check everything else yet. One of the most common mistakes is when taking the adjoint of |0> + i |1> which should be <0|-i<1| but I'm guessing you didn't make that mistake.

How do you know? You haven't done any calculations. You really don't know any of that. As Markus has just pointed out, you're using relabeling of coordinates to claim some physical effect, which is deeply mislead. You're confusing active and passive transformations. I made other points about continuous vs discrete transformations, as well as discrete transformations not being possible to interpret kinematically, which you have chosen not to address, even though they came from comments you made and I read quite carefully. At least much more than their internal logic --or lack thereof-- deserves.

Yes, it's almost as if it's all a matter of how much you perceive the other side is clutching at straws really. I have to say I do not really like this kind of physics of impossibility theorems, of what is possible and what isn't. In pure mathematics, everything is crystal clear --technical difficulties apart--. Your premises are what you say they are. In physics, on the other hand, it seems as though it were always possible to relax the hypotheses some way or another, even at the cost of making extremely unnatural or strangely contrived assumptions. IMO, people who are working on SD are living dangerously, while people who prefer to think in terms of multiple realities are too narrow-minded. Some synthesis will appear eventually and it will feel like "how could we not have thought of this before?" It's obvious to me that's dropping some implicit or hidden assumption that has been invisible to us so far.

Well, I cannot be sure 100% of what they mean. But I would say that they must be implying that all information that determines what polarisation direction the experimenters are going to measure is somehow "diluted" in the dynamical information that's been going around for billions of years, and that information can be "tapped" locally at the moment of the measurement actually being performed. I cannot conceive of any other sense in which they can be speaking. IOW, information can propagate strictly locally, and yet have had plenty of time to reach every corner of the universe, so to speak.

Again, no. We won't get past this. I see how you would think breaking of a continuous symmetry transformation, like time translations, would affect energy. But T as in "CPT" is a discrete transformation. So its breaking has no implication whatsoever on the sign of energy, or on anything about energy for that matter. You need to understand physical principles better. It's amazing how you ignore what you quote yourself (highlighted by myself above.) Here is the complete quote: In other words: to avoid negative energies, we choose a time inversion operator that is antilinear and antiunitary. In no way do we accept negative energies, as that would lead to an unstable vacuum. If you actually read Weinberg's paragraph that you quote it cannot be made any more obvious. The fact itself that we're forced to choose antilinear operators to represent these "reshuffling" of states says very clearly that it's a very different beast. In particular, not amenable to a kinematical interpretation, as you previously claimed.

Oh I see. It's not a sky prince above the clouds. It's a professional up there above the glass. That changes everything. Disprove. Redraw. Otherwise enjoy your radicalisation.

Why would that be? You're using the term "symmetry breaking", which means something different from what you think it means. If by T symmetry being broken you mean there is no exact T symmetry, I don't see why that implies the gravitational interaction changes sign. In fact, we know of a (slight) violation of T symmetry in elementary particle interactions. But both gravitational mass and inertia seem to be unaffected in the way you seem to claim. I don't think you mean gravitational interaction changing sign (that would be because of gravitational mass changing sign). I think you mean inertial mass changing sign, as studied by Bonnor et. al. From the looks of it. The whole thing looks like a rehashing of dead thread: by muruep00, your old self. After a somewhat lengthy discussion, you were told, Doesn't look like you've come up with any maths supporting these intuitions. Copying and pasting the Schwarzschild solution and the relativistic EM equation really doesn't do it, does it?

Anti-orthocronous Lorentz transformations, parity transformations and the like cannot be understood kinematically. They do not relate inertial frames. It's always possible to shift continuously from a kinematical state to another. It's not possible to invert time in a continuous way. It is designed to violate CP, as that's what's shown in B meson decays. As CPT is an exact symmetry of Nature, violation of CP is tantamount to violation of T. There are no negative energy particles really nor does the theory say so. The Hamiltonian is positive definite in QFT. "negative energy particles" is some kind of slang for "antiparticles" that might have crept in here and there due to certain criteria in the Feynman propagator. Actual antiparticles always have positive energy, and so it appears in calorimetric etc experiments.

There is absolutely no problem in extending GR to include anti-orthocronous Lorentz transformations. GR is invariant under the whole group, not only the connected subgroup. It's the standard model that's in conflict with T, P, CP, not GR.

All words and no maths make Jack's a dull toy

Yes, @Eise. You've just kind of voiced my concerns here. I don't know in detail about those critical voices, but I'm sure they must sound something like this: So we have to accept that, even though everything in the universe thermalises very quickly, somehow this information, which is dynamical in nature, must be protected from thermalising so that one day in a laboratory in, say, Vienna, a physicists chooses a polarisation direction and the universe conjures up that information? While not impossible, it rings totally wrong. It goes against everything else we know about entropy, the arrow of time, etc. Degrees of freedom thermalise, mix, get blurred out with time. What magical DoF's are these?