I noticed the link I gave did not work, here is another attempt:
A Novel Approach to 'Making Sense' out of the Copenhagen Interpretation
Armin
I noticed the link I gave did not work, here is another attempt:
A Novel Approach to 'Making Sense' out of the Copenhagen Interpretation
Armin
Dear Akinbo,
I hope I did not offend you with my tough questions. In my view, perhaps the most valuable function a contest like this can serve is that we can provide each other constructive feedback. Compliments and such are nice, but how much do we really learn from them?
My purpose in asking those questions was not to put your idea down, but to suggest areas which, if they are addressed, will make your ideas that much more potentially successful. I revisited my post to check if I inadvertently used condescending or insulting language. I began my questions with:"I think that you will need to provide answers to some of the questions below before more people will take this idea seriously" and ended them with "Your writing style is very lucid and if you can find satisfactory answers to these questions it would make your position much stronger."
So, I don't think I did, my feedback was genuinely meant in the spirit that we can all learn from each other if, when we notice some potential weaknesses or problems in each other's ideas, we share our insights. In that spirit I am perfectly happy to field tough questions from you. My only regret is that you are asking me about General Relativity, an established theory. It would have made me even happier if you had asked me a "head-scratching question" about my own ideas, but here we go: [btw, you are welcome to ask any expert you like to join the discussion, I'd rather have my statements checked by such a person than not]
I have the impression from the way your worded your question that you are still in a subtle way thinking about some underlying absolute rest frame, but, as you know, in GR there is no such thing. Coordinates are totally arbitrary. It is therefore more illuminating to first consider your question in a frame in which the body is at rest. Assuming the body is spherically symmetric, non-rotating, and without a net charge, and gravitational fields from other bodies can be neglected, the Schwarzschild solution would appropriately describe this situation. The solution tells us that the curvature of space-time extends in a spherically symmetric manner radially outwards from the body and vanishes at infinity.
Let us now imagine that we transform to a frame in which the body is moving. As you know, since according to special relativity moving objects will be observed to be length contracted, we should expect a similar effect here, but the difference is that whereas in special relativity spacetime is flat, here it is curved. This means that the Lorentz transformations could only be applied to infinitesimally small regions because only in that limit can spacetime still be considered flat. The overall result would then have to be patched together from the transformations in those infinitesimally small regions. Although I have not consulted a reference on this, I believe that the net result is that in the moving frame the body would no longer be spherically symmetric . This would imply that that the gravitational field would also not be extending in spherically symmetric manner from the body. Although one would need to do a calculation to be sure, I would guess that the shape would be ellipsoidal in that frame.
Now to your question: The speed of gravity is generally assumed to be the same as the speed of light, but in this situation it does not matter because the body had already set up a gravity field before we even considered it. So the "perturbation in space and time" essentially moves at the same speed as the body as long as we consider just rectilinear motion. I think that in frames in which the body is also rotating additional subtleties may come into play. So, of the choices you have given me, it seems that 1) describes the situation fairly, as long as you remember that the range of gravity is infinite. This means that in a sense, in that frame, the curvature of all of spacetime changes as the body moves. Although the finite speed of gravity implies that far away regions will "find out" about the change of location of the body with a time delay, keep in mind that in those regions information about a change in the previous locations was also transmitted with the same amount of time delay, so that there is no net time delay in the local change in curvature far away from the body (i.e. all the changes occur with the same time delay).
Now to your question about MMx. I think this is a truly excellent question. The frame in which we would normally consider the MMx is the one in which the body is stationary, and hence the gravity field is symmetric. Neglecting any variations in the gravity field due to inhomogeneities in the density of the body or of its surface, I would say that in that frame the gravity field should have no effect because space, though curved, is still isotropic and this is one of the key assumptions on which our understanding of its results rests.
However, as mentioned above, when MMx is considered in a frame in which the body is moving, then then the gravity field is no longer extending radially outward in a spherically symmetric manner in that frame. Let us imagine interferometer arms that are sufficiently long and suppose a sufficiently sensitive detector of fringe shifts for the following argument: Since the field is no longer spherically symmetric, neither is the field strength. According to GR, light is observed to travel more slowly in stronger gravity fields (The speed of light is still c locally, where, because the observer himself is subject to the same gravitational field strength, this effect cancels out). So if this is the case and a light beam traveling in one direction encounters a different gravity field than another one traveling in the perpendicular direction, then this should affect the relative travel times, and this should be detectable via a fringe shift. But the effect is frame-dependent whereas whether a fringe shift is detected or not is not frame-dependent.
Is this a paradox? I have never read about this situation anywhere, nor thought about it until you asked the question, so see what you did, Akinbo? Good job!
The only way to be certain is to actually do the calculation but I think there is no paradox. Rather I suspect that the resolution lies in the fact that the same Lorentz contraction that was responsible for changing the gravity field in the first place also introduces both length contraction and time dilation effects which effectively cancel gravitational effect, so that the net result is no fringe shift. However, because the effects we are talking about are non-linear, it is possible that my answer is wrong or incomplete.
I would be interested to see what the experts have to say on this (though I have had a GR course and one on the philosophy of GR, I am by no means an expert on it).
Well hope you are satisfied, it just may be that more people than just me will be scratching their heads, ha!
All the best,
Armin
Hi Armin,
Thanks for your detailed response in my thread, really much appreciated. Of course you are right about the presentation(last minute jobs are always lousy), I will prepare some material for you in the next day or so and see if I can be more convincing.
Regards,
Adel
That post is mine, I did not log in !
Not sure what is going on.
No no no! I Love your criticism, with a capital L. In fact most of what obtains here amounts to mostly unmerited flattery. I am equally guilty. Hardly would one see comments like yours that make you scratch your head. A few say their mind, one of whom is Joe Fisher. Uses the word codswallop to tell you if he feels what you say is not okay with him. ITS ALL A GAME!
Lets enjoy it.
Best regards,
Akinbo
Dear Armin, what an excellent essay and as I noted in your answer to Giacomo, you wrote; "All it expresses is that one can have at minimum a bit of information if it is possible for something to take on distinct values." I agree completely with this assessment and may I point out that in KQID, this one bit is the Wang Yangming one bit as the unity of Giving and Taking. I did reply to your question in my forum but knowing how busy you are with other matters, I repost again in this forum. Answering your question: yes, I found it is extremely difficult to do so many things at the same time and I have been blessed to be able to do what I am doing. However, I must work days and nights literally with all my being all my life to conduct this research that I love. I share deep empathy to my fellow seekers of the truth in this FQIX wonderful and creatively talented community, Tianming Ren(people). I do have an advantage that because of my wide experiences in business, economics, international affairs, philosophy and law, I am NOT captured and kidnapped by orthodox meme that controlled unawared minds. Even those awared minds are extremely difficult to escape from their learned and adopted views that run successfully their everyday lives. Our billion years of evolution teaches us to be cautious from any new idea. Now on KQID, KQID prescribes that bit is it: bit=it. This bit or this it is bit-waves, so musical tunes. It is Pythagorian in steroid that all things are one Qbit as the only singer or the only pianist like you who plays all the musics accompanied by its myriads Tianming hologram clones and drones simultaneously as singers and spectators. It observes itself and collapses its bit-wave function. This Qbit is the one and only singularity Qbit Multiverse. You and I sing our own songs and dance our own Gangnam style moves like those scout bees doing theirs dances communicating their discoveries of new food sources for the survival of their colony. We project our desires and lusts naked out there space-in-time to be manifested in myriads forms and substances like a Ferrari Enzo. What a wonderful world! What a magical world! What a beautiful world! Mesmerizing to those who open their hearts and minds to see, touch, taste, hear and think nature as IS. Is as IS naked fresh raw salad. KQID prescribes Existence in the Ouroboros Equations as FAPAMA snake Qbit eating its own tail. The FAPAMA Qbit is self-bootstrapping to will itself into what we collective feel alive. We talk, walk, run and make love. KQID is physics and more. KQId is an operating system of Existence. KQID offers not only a new window to see things differently but KQID recreates and redistributes our Multiverse in our own image literally. We the Homo sapiens create and distribute our own Erosverse that encompasses all our relationships with our selves, family, community, mankind, aliens, cyborgs and robots and our Multiverse. We create and distribute our own world in our own image literally. We are Tianming Ren (people) endowed with super power of nature. Let us work together to bring peace and prosperity in our world we share and love. Best wishes, Leo KoGuan
Dear Armin,
I read your lucid essay with enthusiasm and found myself surprised to know that we both share common views in analyzing the relationship between It & Bit in all three fields of physics. Yours' is an elegantly written essay by analyzing the relationship existing between the 'back ground material' on one hand, and It & Bit on the other. I am curious to know how you make use of 'default specification principle' in your further research work to solve amicably the problem existing between It & Bit in both classical physics and the quantum one. Because of similarity in our ideas, I would like to rate your essay with maximum honors.
All the best in the essay contest,
Sreenath
Dear Armin, very perceptive of you to notice that KQID can be "practically implemented as a philosophy for living". KQID is designed as an operating meme that is looking for WILLING hosts to adopt it and allow the meme living within and operates the task of helping the hosts to decide using Wheeler's series of questions a yes, or a no or maybe. This way to assist the host to realize his/her dreams and aspirations. As my answer to Brian above that I sing and praise the Xuan Yuan's Da Tong based upon the greatest discovery of the Yellow Emperor's Four Cannons buried in 168 B.C in Mawangdui near Changsha in 1973. The Grand Historian Sima Qian reportedly around 100 B.C that Xuan Yuan (the Yellow Emperor) text was lost already and he could not find it anywhere. Thus for more than two thousand years Chinese scholars did not have access to this mankind's treasure. Xuan Yuan is the founder of modern Culture-Nation China about 5 thousand years ago, he at that time laid down in blood the first Chinese Constitution: the Mandate of Heaven that anyone has the right and duty to take down a tyrant ruler and killed him as he killed and skinned the tyrant Chi You He also conceptualized Chinese rule of law and principle jurisprudence that from Dao comes law and virtue and no one is above the law and virtue and everyone including himself and all kings and ordinary persons are treated equal under the law and virtues derived from Dao. Dao is the Heaven Law of Nature. With an operating rule of law and principle nothing that cannot be curbed. This is not all! He preceded Thomas Jefferson by almost 5000 years in which his mission in life as well as the mission of his Culture-State is to help each person to realize his/her dreams and aspirations, if he/she does not have one, he will work together to find one. However, no matter what he will help everyone to have good education, to be healty and rich. This idea later on became the credo of Chinese Dream that I believe what President Xi Jinping eloquently speaks out as he and his adminisration would like to accomplish.This is what Kongzi (Confucius) advocated and he took Da Tong poetry, Chinese Dream, from the Book of Poetry that he laboringly collected around 500 BC in Zhou Dynasty. Thus since Xuan Yuan era 5 thousand years ago, China has already advocated Chinese version of Rule of law and principle and we are still working on it to make it better and better everyday. The written constitution of this Jurisprudence is the Mandate of Heaven. My study of Dao leads me to my KQID theory as the foundation of the Scientific Outlook Rule of Law and Principle that on top and with KQID powerful engine we build Scientific Outlook Free-Lunch Economic System that will enable everyone to have free education, free health care and free material wealth. So that we become super Tianming Ren(persons) endowed by Nature(Dao). I am a practical person. This is NOT a pipedream but a realistic goal that we can achieve soon. At the same time, KQID is truly physical theory that not only about an operating system of Existence but also about predictions, verifications and falsifications. The KQID Ouroboros Equation of Existence: Ξ00☷ = ψτ(iLx,y,z, Lm) = KbΘln2 = hf = pc mc^2 = p^2/2m U(iLx,y,z) = 4πGρ- Kqid(ΑΘ-ΘS)gμν = (8πG/c^4)Tμν - Kqid(ΑΘ-ΘS)gμν = Τμν = E = A S ⊆ T that contains QM, KQID relativity, Landauer's bound, Planck, Einstein, Newton, Maxwell, Poisson, Einstein GR with KQID dark energy equation and KQID Third Law of Multiverse as the equation of everything from physics to chemistry, law, monetary and full employment. In physics as shown in my essay, this equation explains the Bit Bang, not Big Bang, plus its partner the Bit Crush and we can estimate the temperature about 7.8 x10^126K in the first burst at 1.43478x10^-147 seconds with the wavelength λ = 4.3x10^-139 meter, moreover when A = S our universe will inevitably start its contraction and acceleration to a Bit Crush sometime hundreds of trillions years later thatI also calculated in two different ways. As you can see I made specific predictions with specific numbers that can easily be falsified later by experiments. We are the seekers of the truth and paraphrasing the great Carl Sagan, we are the Qbit's way to know itself and to evolve as a renewed Qbit every absolute digital time T≤10^-1000seconds. We are brothers and sisters literally in our human senses but actually we are one in our Ancestor Qbit reality. Thanks for asking questions and I am grateful for your kind interest.
Sincerely,
Leo KoGuan
Dear Sreenath,
Thank you for your comments. The paper that introduces the framework that is based on the default specification principle can be found here:
A Novel Approach to making sense out of the Copenhagen Interpretation
If you cannot it download it from there, you can also find on public repositories it by just googling the title.
This paper only presents the first step, as there is still much to do. Here are some of the areas where I need to do more work:
1. Tighten the mathematical connection between the axioms and the derivation of the path integrals
2. Derive path integrals for situations other than the free particle.
3. Connect this framework directly to the Born Rule
4. Generalize the framework to quantum fields
5. Derive precision predictions that distinguish the theory empirically from others
As you can hopefully see, this is a full-blown research program, but right now I am pursuing it on my own time with my own funds part-time. For that reason progress is not going to be nearly as fast as I would like, but I believe that even already what I have now is stronger and more promising than the ideas that are pursued in mainstream research. Of course you would expect me to say that, but I invite you to read and try to really understand the framework so that you can check for yourself.
All the best,
Armin
Dear Armin,
Thanks for your clarifications.
All the best,
Sreenath
Dear Armin,
This does not really apply to you as I have rated you high already. Moreover I will be revisiting your blog after the contest. Meanwhile...
As the contest in Wheeler's honor draws to a close, leaving for the moment considerations of rating and prize money, and knowing we cannot all agree on whether 'it' comes from 'bit' or otherwise or even what 'it' and 'bit' mean, and as we may not be able to read all essays, I pose the following 4 simple questions...
"If you wake up one morning and dip your hand in your pocket and 'detect' a million dollars, then on your way back from work, you dip your hand again and find that there is nothing there...
1) Have you 'elicited' an information in the latter case?
2) If you did not 'participate' by putting your 'detector' hand in your pocket, can you 'elicit' information?
3) If the information is provided by the presence of the crisp notes ('its') you found in your pocket, can the absence of the notes, being an 'immaterial source' convey information?
Finally, leaving for the moment what the terms mean and whether or not they can be discretely expressed in the way spin information is discretely expressed, e.g. by electrons
4) Can the existence/non-existence of an 'it' be a binary choice, representable by 0 and 1?"
Answers can be in binary form for brevity, i.e. YES = 1, NO = 0, e.g. 0-1-0-1.
Best regards,
Dear Sir,
We are extremely grateful to you for the time you have devoted to explain the points raised by us. But it has introduced new questions requiring explanation. Hence we request you to kindly clarify our doubts.
When you talk about spatial derivative and a field, we presume it is a three dimensional field, of which you are considering only the x-axis. Position must refer to the placement of an object, which also is 3d. But if an object is moved along x-axis in a field, does not the change of co-ordinate affect the other coordinates of the body like y-axis and z-axis? If you vary the radius (around center of mass) along x-axis, the volume increases by 3 orders of magnitude. If you drag the object along x-axis, the distribution of mass and energy in the field changes changing at least the gravitational interaction with other bodies in the field (or space-time curvature). Can we eliminate these effects since there are no perfectly isolated objects? If not, whether these have been included in your description? Then where and how? You say the constant need not be zero. But it has to change as shown by us above - hence it is not constant. You also say, "If dF/dx is larger than zero, then the Field strength increases as you go farther along x". Increase in field strength implies increase in energy. Where from this energy comes? If it is redistributed or additional energy applied to the field, then it will affect not only other bodies in the field, but also the field strength itself.
We do not understand "rate of change of the rate of change". Once a force is applied to move the body along x-axis and the body moves, the force ceases to act and the body moves at constant velocity due to inertia (assuming there are no other forces). The new velocity can be v'. The relation between the original velocity v and v' is the rate of change. To accelerate the body further, you need another force to be applied to the body. If it moves along with the body, then it cannot accelerate the body. Without such a force, the body cannot be accelerated. What is that force and from where it comes? If another force is applied, it will change the velocity to v''. The "rate of change of the rate of change" would mean relating v to v'' and so on. But why should we compare these with v instead of v'?
The classification of time independent and time dependent is not understood by us. Can we eliminate time from any physical description? If we talk of constant energy, then we have to consider the whole universe or its replica. Thus, the Schrödinger equation is valid only for hydrogen atom and not others. We have already said that complex numbers are hypothetical and not physical. It is like adding horn and rabbit to describe the horns of a rabbit, which is physically not permissible. Hence, they cannot be used in computer programming.
Incidentally, most people have changed their impression about us after reading our essay. May be you will also change if you read it!
Regards,
basudeba
Hello Armin,
I mean to read your paper in much more detail. You left a nice comment by mine, and someone else mentioned your paper as well. There are some similarities. I thought I'd start with the very general philosophical issues that may be confusing.
In your section 2, you imagine a world without distinctions, described by a single arbitrary number, or a number repeated. Such a world, without distinctions you claim, does not need any information to represent it. I am wondering if the situation may be a little more slippy.
In my essay, I started out with the claim that a Bit is essentially symmetric because it represents a distinction but just what is it that is separated by that distinction is irrelevant. Now maybe people now have two concepts of Bit in their heads, the Shannon ideal that it summarizes something else and thus communicates information, and the practice of computing, in which the user of the computer has access to inquiring, given an address, to whether a 0 or 1 is present.
So back to your situations. What if you had a world without distinctions and you chose the number 0 to represent it (you say the # can be arbitrary.) And then what if instead you chose the number 1, as you say repeated arbitrarily. You say that there is no information to distinguish and yet you've produced a bit (choice between 0 or 1).
Hi Armin,
Your comment at the end of the essay "the boundary conditions are due to actual spacetime objects ... [which] must be counted as features of the background" brought to mind deBroglie's pilot wave theory. He could account for phenomena like the double-slit experiment by assuming that the slits themselves had a quantum potential which guided the path of the photon or particle. I suspect a good part of the reason pilot wave theory was neglected until Bohm's rediscovery of deBroglie's work in the 1950s was that it implicitly allows a quantum potential for the background by the argument you noted. Bohm called the background the implicate order, which is aptly vague. Pauli's famous quip "It isn't even wrong" was made about Bohm's paper, which tells you how it was received at the time.
I am not sure how this might relate to the premise of your essay, but it does concern the question of background. If you are interested, Mike Towler's lectures on deBroglie's pilot wave theory and the foundations of QM are at this website. (Select "Lectures and slides".) The slides from the introductory lecture give a nice overview of the theory with many of the details laid out. Towler makes an excellent case, and it is an interesting bit of history.
All the best to you,
Colin
Dear Basudeba,
The explanation for the derivative I gave was for a 1-dimensional model meant to highlight the mathematical definition of the derivative. It is perfectly valid to just consider a 1-dimensional model which often avoids the complications arising from using more dimensions.
I regret that I simply do not have the time to further clarify the issues you raise, just typing the explanation of the derivative took me a couple hours. I will note that to me they simply reflect more of the same misunderstandings I mentioned before. If you really want to contribute to the discussion in fundamental physics in such a way that it is taken seriously by the professionals in the field (of which I am not yet), then you need to make sure you understand calculus and quantum mechanics at a quantitative level, which they would consider elementary pre-requisites. You may wish to hire a tutor, to whom you could show our exchange and then direct your questions.
I did look at your paper, and unfortunately it did not change my mind. It appears that you know a large number of isolated physics facts, but that you have large gaps in understanding how they relate to each other. I believe this would become quickly obvious to any physicist, and after encountering the first couple misunderstandings, they would be unlikely to spend any more time considering your ideas.
I know that my assessment may sound very blunt, but I believe that in this environment in which it seems many just try to sugarcoat their true opinions either for fear of retaliation or to gain a high vote, it is all the more more important that you receive an honest assessment.
I wish you the best and hope that you will take the advice to heart,
Armin
ok, 1110
On 2) I assume you meant to say "...can you in principle 'elicit' information?"
On 4)I actually have a paper in preparation, tentatively called "Quantum Mechanics and Existence" in which I challenge the binary conception of existence.
All the best,
Armin
Dear Bram,
Thank you for your post, you raise a rather subtle point. I agree with you that "just what is it that is separated that distinction is irrelevant". Where we seem to part ways is that once you have fixed some kind of meaning to the representation of one of the possibilities, however arbitrary a distinction it represents, the representations of alternatives are then immediately constrained by that choice, and if this not taken into account, can result in an incorrect representation.
Take your example: the first choice is to represent the world by 0, the second is to represent it by 1. However you choose to represent it doesn't matter (this is our point of agreement), but once you mix the two representations to create a "bit" then I see a problem: because 0 already represents that world, making it part of a "bit" in which 1 also represents the same world leads to one of the two possible results: if you consider the bit in the usual sense that 0 and 1 represent alternatives then this implies 1=0 because the alternatives represent the same thing. If you mean that they need not necessarily represent actual alternatives, then this implies the strings 10 and 01 mean the same thing and they could both be more simply represented by, say, 0, which still falls short of a single "bit". This is what I meant when I wrote: "whether one considers such a string a sequence of single digit numbers, or just a single number by itself, or anything in-between, is completely arbitrary.Insofar as the numerical encoding of such a world falls short of even a single bit (because none of the digits have the possibility open of taking a different value), we may consider distinctions to be a prerequisite for the definition of information."
Perhaps it helps to also consider the following example: Take any yes or no question and represent it in terms of binary numbers. The common choice is 0 for no and 1 for yes, but one could also choose 1 for no and 0 for yes. Now, what you are doing seems to me analogous to creating a new "bit" by combining, say, the 0 from the first choice and a 1 from the second. But they mean (i.e. represent) the same thing, therefore the new "bit" no longer represents the yes or no question, as both choices mean no.
There is a way around this (sort of), and this is where the subtleties arise (And this may be what you had in mind). You could assign the first bit (0 no, 1 yes) to "Armin's representation of the yes or no question" and the second bit (1 no, 0 yes) to "Bram's representation of the yes or no question". Then it is perfectly alright to mix the representations, but you notice, the meaning of the newly created bit has changed: It no longer represents the original question. Rather it represents a choice between my representation of the no answer and yours.
In my essay I was, however, not concerned with these meta-levels of meaning that representations of distinctions could acquire but just with representing physical distinctions directly in such a way that whatever means of representation is chosen correctly represents those distinctions. I believe your example does not do that because it either implies a contradiction or it is not a true "bit".
I hope that I was able to clearly explain my viewpoint. Thank you again for your engaging question, and if you have a rebuttal or more questions, I'd love to hear it.
Armin
Dear Colin,
Thank you so much for reading my paper. The statement you quote is actually an oversimplification of what I really think, but trying to explain the nuances of that idea would have taken more space than was allowed under the contest rules (I was only about 100 characters under the limit).
I must say that any connection between Bohmian mechanics and my framework escapes me. If my rudimentary understanding is correct, there the quantum potential serves to guide the particles which are "hidden" so to say, behind the wave function. As you know, in my framework there is no underlying "particle" (at least in the sense of a spacetime object), the wave function is really it (at least for us spacetime observers). It is possible that I might arrive at some similar pieces of mathematics, but if so, the meaning would be completely different. At any rate, I believe a truly detailed and representative account can only be given in terms of field theory, and I am still (very unfortunately) quite a bit away from that. Thanks again,
All the best,
Armin
Dear Sir,
Thank you for this reply which conforms our belief that faced with an awkward question, scientists claim superiority of their knowledge and denounce others, but never try to reply to the question. The time you spent in writing the post could have been better utilized have you tried to understand our question. For your benefit, let us educate you on the meaning of what you have written and some basic physics.
Dimension is the perception of the differentiation of the internal structural space from the external relational space of a particle. Since we perceive dimension as form through our eyes by electromagnetic radiation, where an electric field moves perpendicular to a magnetic field, both of which are perpendicular to the direction of their motion, we have three mutually perpendicular dimensions. They determine the state of the substance: if fixed - then solid, if fluid - then liquid and if loosely held:then gas. Thus, the concept of one dimensional model is nonsense. You have not understood the concept of dimension - hence used it as a direction.
Please try to learn your basics before recommending us to go to a tutor, who will repeat what he has been told in the text books without understanding its meaning like you have done here. We do not follow others blindly and claim ourselves a great scientist. We lead independently. We are not here for recognition - we want to understand Nature. If you have any queries, you are welcome.
Regards,
basudeba