RELATIVITY+ I’ve always held Albert Einstein in the highest regard. I admire his ability to think outside the box, and empathise with his curiosity and desire to understand the world in terms we can grasp and understand. Interestingly, when you read about Einstein, you realise that some things are incorrectly attributed to him, and there have been some subtle but crucial shifts in interpretation that he wouldn’t agree with. If Einstein was still alive today, I think we would have a different interpretation of Relativity. I think he would have explained the postulates he used in Special Relativity and General Relativity, and would have united both theories into something new. I’d like to introduce you to my vision of where Einstein would have gone. I’ve given it a name that is easy to remember and hopefully conveys the right message: RELATIVITY+. There’s already a General Relativity+, but I want something even more general, and RELATIVITY++ isn’t so easy on the tongue. We start with time. Albert said “time is suspect”, but we’ve rather forgotten that. We’ve also rather forgotten his Princeton years with Godel. We misinterpreted Godel’s rotating universe as something that permits time travel instead of rendering it impossible, and we have brushed aside Einstein’s conclusion. The TIME EXPLAINED essay below describes how time is a relative measure of change, and whilst it's a dimension in the measure sense, it really isn't a dimension like the dimensions of space where we have freedom of movement. It exists like heat exists, but like heat, it is a “derived effect of motion” rather than something fundamental. TIME EXPLAINED Time is the guilty party. Because once you understand time, you hold the key to all the doors in Physics: Spacetime is a Space. It’s rather difficult to accept this, because it’s difficult to analyse your own long-held concepts. There are psychological factors at work, associated with the phrase “Catch ‘em young”. Since ”Time is Money” and as an illustration why you should persevere, I offer an essay MONEY EXPLAINED: MONEY EXPLAINED No, time is not money. But it isn’t quite what you thought it was, and if you can accept this you’re starting to understand ontological thinking. It’s a matter of looking at what’s really there, and asking yourself soul searching questions about the concept you hold dear. In the picture below, squares A and B are the same colour. Sounds amazing, but it's true. Follow this echalk optical illusions link to check it out. Please Register or Log in to view the hidden image! One such question is: ”If I understand it, can I explain it?” If you think you understand something but you can’t explain it, then you don’t understand it. You perhaps already understood money, and you may already be aware of some parallels between money and energy. But do you understand energy? ENERGY EXPLAINED Please Register or Log in to view the hidden image! Energy is in essence stress, quantified by volume. It’s that simple. In empty space with nothing to hold it in place, a stress travels, like a ripple in a rubber sheet. We call it a photon. It has momentum. But it’s all relative. If it’s the photon moving, you feel its momentum when it hits you. If it’s you moving, you feel its inertia when you hit it. When you really understand this relativity, you understand just how simple mass is: MASS EXPLAINED Please Register or Log in to view the hidden image! In its barest essence, mass is energy going round in circles. When you push an object you deform these circles in the direction of motion, creating a partial spiral. The energy now moves in a helical fashion, rather like a spring. To stop the object you have to push the “springs” back into circles. It’s wonderfully elegant, and what’s more it tells you that everything is basically made of light. We live in a “hard light” world. Everything is drawn in light, and when we measure the speed of it, it’s like we’re measuring the length of our shadow with the shadow of our ruler. We can now understand what Einstein meant in chapter 22 of General Relativity about the non-constancy of the velocity of light. And we can now understand Gravity: GRAVITY EXPLAINED Gravity is not really a force. That’s why unification was so difficult. It’s like an extended tension gradient opposing matter/energy stress. The speed of light is always 300,000km/s but light defines our time. The speed of light isn’t constant, and that’s what the gravity is. There’s no magical mysterious spacetime curvature. Not when spacetime is a space. Not in a world drawn in light. It’s just the permittivity of space that changes. The capacitance. The thing we call c changes, it is not flat. And it all comes down to charge, which is a story of something and nothing. Understanding this is the next challenge. And once we understand it all, we can set to work. And if we can make it work, we’re on the road to the stars. And I like to think that the name of the road is: RELATIVITY+. © “Farsight” 2007
Ok, Farsight. I will read your post and comment only if we can agree on common ground. First, What is the algebra governing space-time transformations? You treat sace and time asymmetrically, so one cannot use the Lorentz Group anymore.
Can we also agree to abide by Alpha rules on this thread? I can't give you your answer. You will be aware that I'm not a professional physicist, and not a mathematician. I trust however that the lack of mathematics is not an insuperable problem to you - on the Lee Smolin thread you did say the theory was ten years ahead of the maths. http://www.sciforums.com/showpost.php?p=1329311&postcount=24 Also note that the primary issue here is not the mathematics, but instead the axioms upon which it is built. Thus I'd hazard a guess that any mathematically formalised version of these essays would be familiar to you. http://en.wikipedia.org/wiki/Poincaré_group Meanwhile feel free to use mathematics if it assists you in any way. Whilst no expert, I'm not illiterate. If I can commence with "the first thing" about space and time, read the first essay, TIME EXPLAINED, and perhaps you'll understand why I say: Minkowski was wrong. I look forward to your reasoned comment and open debate.
But if you can't understand or formulate your statements at an empirical level, how can you make statements like "Minkowski was wrong"?
You will find that I have a very short memory. Don't accuse me outright of not knowing anything about space and time and we will be fine.
The point in asking you the question was for me to see what I am dealing with. I have my suspicions, but I need to understand at what level to construct my rebuttals.
You should check your references. General Relativity subsumes Special Relativity. Special Relativity is General Relativity without acceleration. http://en.wikipedia.org/wiki/General_relativity In this post, I am trying to understand whether it is your position that General Relativity and Special Relativity NEED to be reformulated into a different theory.
No problem with the subsumes. OK I shouldn't have used the word "united", but wanted a hint of TOE. I wouldn't say reformulated into a different theory. I'd say developed. If you look a Newton's "Theory of Gravity" he doesn't actually explain what gravity is. Special Relativity doesn't explain its postulates. And General Relativity doesn't actually explain gravity. Of course, we tend to say "gravity is curved spacetime", but when you actually look at this, can you genuinely say that this is an explanation? If we really understood gravity, would we still be using rockets?
Those theories are mathematical representations of interactions and how they affect - they were never meant to explain what they were.
Is this what you are claiming? If so, then I find this difficult to believe as you (admittedly) don't understand the maths involved. I don't understand the maths involved, and I've been studying Grand Unified Theories for four years. If you want a unified theory a la Einstein, I think you are bound to fail as Einstein himself did. The point is that we know quantum mechanics is an essential ingredient in our universe. But there is absolutely no way that GR can be made consistent with QM in the normal way. For this you need either string theory or something esle (i.e. Euclidean quantum gravity or Loop quantum gravity). This I agree with, and it drove Newton crazy. Like (Q) said, this is ok. You make a set of assumptions, and then you see what happens. Einstein took two assumptions for SR, and one (?) additional one for GR. In so doing, he derived things that are completely consistent and experimentally verified. And curved space time is a beautiful explanation. The idea that matter and energy are bound to the undelrying fabric of some Euclidean manifold is beautiful in its simplicity. Einstein's equaitons say geoemetry = matter...that is, the mere presence of some non-trivial energy density means that there is gravity. The fact that GR fails when you try to quantize it is dissapointing in some sense, because the classical beauty of GR doesn't carry over into the quantum world. Hmm. Just because we understand something doesn't mean we can manipulate it.
I'm not claiming a TOE, that would be too much. Yep, curved spacetime sure is a beautiful explanation. But I think it's wrong. To keep you sweet, I'll tone that down to lacking. You have to really "get" the TIME EXPLAINED essay to realise why I say this. It's not easy, because you're having to analyse a concept you take utterly for granted. There's definitely some strong "conditioning" psychology going on with this sort of thing. For example: you and I think suicide bombers are crazy, right? They don't. Edit: See this Einstein's Gravitational Field paper by Pete Brown (pmb). I can't claim it as authoritative, but you might find it more persuasive than something you read from me. If GR fails when you try to quantize it, maybe the problem is something subtle. I can't claim any expertise on QM, but maybe you shouldn't try to quantize it. Or maybe a shift in interpretation here or a little tweak there will bring things closer. For example, flip the infinite time dilation at a black hole event horizon into a zero c. Then there's no need to renormalise it under the carpet, and voila, you've got Frozen Stars instead of Singularities. Yep, understanding something doesn't mean we can manipulate it. But we've got a better chance if we do. Shades of Podkletnov I know, but I do wonder how I can achieve a high local energy density.
But what basis do you have to make this claim? The fact is that classicall, the curved space-time picute has never been invalidated by experiment. This means that it is the correct picture. Untill someone can preform an experiment that shows the interpretation fails, it is the one that should be accepted by science. Einstein's equaitions say geoemetry = matter. That's it. The presence of matter (or, more generally, energy density) causes a non-trivial geometry (i.e. curvature), therefore causes gravity. The point is, you have absolutely no grounds to judge the interpretation of gravity as cirvature as 'wrong'. Of course I don't get it! I haven't spent as much time as you thinking about it. I don't have a degree in physics or anything. Oh wait... Before I jump in to trying to see the world with your interpretation, I want to esablish the motivation. And I so far you haven't been at all convincing. You say "The interpretation of space-time as curvature is wrong", but it is the correct interpretation in terms of agreement with observation. It is the natural implication of Einstein's equations. But this is the point. GR is formulated in terms of an Euclidean manifold, and manifolds (by definition) don't have singularities. That is, the only place that GR possibly could fail is when you look at places of infinite energy density---i.e. at the center of a black hole. In quantum field theory, it depends on the type of singularity you get---if something looks like log(big#), you're ok. We know how to deal with logarithmic divergences, and we can get fantastically accurate results out.* But GR is a quadratic divergence, that is, the numbers in GR scale like big # squared. But there is observational evidence for black holes, so... It's pretty clear that we will just end up talking in circles, so I think I will just continue reading your essay until I come to the next misconception. I have to say that thus far, your arguments have been far from convincing, although other than putting words in Einstein's mouth you haven't really done any physics in the first two paragraphs. ------------------- *Consequently, in getting such accurate results out, we generally rotate the integrals to a space where 'time' is another 'space' dimension. We can then integrate over 4 spheres, and get an answer that looks like finite + infinity. There is a way to deal with the infinity, and the finite part matches experiment (in some cases) to something like 13 decimal places. In this sense, QFT is more accurately verified that GR.
This is your first violation of physics as we know it. From your arguments in the other thread, it is clear that you view time as manifestly different than space because "you can move around in space but not in time". This is why I asked the very first question about rotation groups. Here's the math lesson I promised youPlease Register or Log in to view the hidden image! The Lorentz Group: Explained First, if you write down the most general transformation in three dimensional space, you have rotations and translations. You can spin around or move around is all this says. Now, rotations are easy to deal with---we know that the group SO(3) describes rotations in three dimensional space, but what of the translations? For example, take a cube. If you rotate a cube about the x axis and then about the y axis, you should find it is the same as if you rotate it about the z axis. Do it with a die, or a Rubick's cube or something. This is the sense that rotations make a mathematical group: rotation about x + rotation about y = rotation about z. It's like even numbers. Every time you add an even number, you get another even number. This is the toughest thing to prove about groups, that it closes under addition. See this http://en.wikipedia.org/wiki/Group_(mathematics). It does seem odd that we can preform rotations according to strict mathematical rules, but not translations. Here you would stop, because translations are basically time dependant. That is, you need a velocity to do a translation, but not to do a rotation. This is a reflection of the fact that boosts depend on the Lorentz Factor \(\beta = \frac{v^2}{c^2}\). (This is a conclusion of Special Relativity because it essentially comes from length contraction.) But now the kicker. If you boost along, say, x, and then y, it is the same as a rotation about z, once you account for the length contractions along the directions of the boost. So we end up with the same cube after two boosts as we do after one rotation. (I can put this in a mathematically more precise language, but I am sitting in a coffee shop reading physics papers, and I do not remember the relevant formulae from the top of my head.) All of this was known to Einstein. So now we have a bit of a wierd structure. The rotations by themselves satisfy the rotation group SO(3). But you can also write group relations between the translations and the rotations. (Again I stress---this was known to Einstein.) Well it turns out that if you look at the translations, and you know a little about group theory, you say "Wait, this is just SO(4)!!!" In essence, what you have realized is the very deep fact that the symmetry group of space is justa subset of the symmetry group of space-time. (We write SO(3,1) to remind us that time is different, but not as different as you think it is.) Physically, this means that time is no different from space, in the sense of the allowed operations on vectors which live in space-time. This is the idea of Lorentz Invariance. You will counter with one of several arguments, a few of which I will anticipate here. The first argument you will present is the same one you gave in the other forum---why can't I travel in time? My answer is, you're not a fundamental particle. When you solve Dirac's equation for an electron, you find a set of negative energy solutions. This is a problem because negative energy is meaningless. But energy is just the time component of the momentum four-vector, so the interpration is clear---the negative energy solutions are electrons moving backwards in time. This is exactly what a positron is. In quantum field theory, one can always show that a consistent theory must be consistent under three symmetries: charge conjugation (C), parity (P), and time reversal (T). The symmetry CPT is shown both analytically and experimentally to always be conserved. Always. So, time is different because you are a classical object, and not a quantum one. The second argument you will possibly use is "Well, how can Einstein think that 'time is suspect' if this is true?" The answer is easy---Einstein never believed in quantum mechanics, which is why his theories of unification ultimately failed miserably. Einstein's genius has only been paralleled a few times last century, but the thing that made Einstein brilliant is also the thing that prohibitted him from ever accepting quantum mechanics. Does this mean that QM is wrong? No, it means that Einstein was, about QM at leastPlease Register or Log in to view the hidden image! One would hope that, at this point in history, Einstein would have realized his mistakes. But there's no way to tell, as Einstein himself laid on his deathbed looking for a unified theory. Lasty, you may try to change the subject because you "don't understand the maths involved". Don't do that. If you want help understanding this stuff I will help you. If you ever in your life want to be listened to, this is part of the language you have to know. The idea of Lorentz Invariance is as central a concept in physics as anything. Without Lorentz Invariance, we don't know how to do physics.
If this is your great insight, then goodPlease Register or Log in to view the hidden image! Space-time is a space. In is a Lorentzian manifold with signature (1,3). This means the metric comes from the Lorentz group SO(1,3) (or SO(3,1), it doesn't really matter). If you're working in string theory, this group is SO(1,9) or SO(1,10) at the string scale. But this means that space and time are just two aspects of the same thing. The idea that time is different from space in your paragraph 3 does not lead to this interpretation.
See the edit to my post above - sorry, I got stuck on the phone and didn't know you were around. My basis, is that your concept of time is wrong. Read TIME EXPLAINED. It's hard to swallow what I'm telling you, but stick with it. Did you check out the colour illusion? The illusion is that squares A and B are different. They really are the same. Your concept of time is something like the colour illusion. Please Register or Log in to view the hidden image! No problem. There's no harm in sticking with the accepted interpretation. But you should still take a look at some development or alternative. As it happens, I like Einstein's "pure marble" geometry. And I think you can get the same results with a different interpretation. I do. Honest. My motivation is: I love physics. There are things out there in space. We've observed them. They're small, maybe planet sized, light traverses them quickly. They're maybe smaller than the Schwarzschild limit. They have terrific gravity, enough to wobble a star. Sometimes we see enormous blasts of X-rays, sometimes we see nothing. They seem to be black. And they seem to be holes. So we call them black holes. But here's the rub: if time dilation is infinite at the event horizon, the c is that location is zero. It's not something you sail through unnoticed in your inertial frame. BLAM. It's a brick wall. It's a Frozen Star. And it's a black hole. But it hasn't finished collapsing yet, and never will. Ergo no central singularity. Two paragraphs? Out of six essays? Nevermind. Please continue. Hopefully you can contribute some useful feedback, and I will be grateful for it, really. And hopefully you will discover is that it's all clear and logical. A piece of cake. A picnic. A Teddy Bear's Picnic.
Farsight---I am going paragraph by paragraph in a review of your essay. The reason I stopped after two paragraphs was that where my first objections occured. The point is you cannot put your ideas on a mathematical footing. This is like saying "I am the world's greatest poet, but I don't speak any English." Without putting your ideas in a firm mathematical footing, as even your beloved Einstein had to do, you cannot in any sense call your theory a description of nature. If you think space-time curvature isn't the same as gravity, then you have to show this mathematically. Read my essay called "Lorentz Invariance Explained", and hopefully you will see that this is not at all the case. What do you consider useful feedback? What do you really want out of this? If I tell you your ideas are wrong, and show you where both the math and the experiments show you're wrong, is this not useful?
No problem. I'm calling it a model rather than a theory, and a toy model to boot. And it isn't easy to put t on a firm mathematical footing. Or E or m or g. Sure, in a formal paper. For now we're only talking about ideas in an essay on a forum. Will do. Anything that relates to the content. Even if it shows me I'm wrong, painful as that might be. As for what I want, I want to contribute to physics, and our understanding of the world. Did you catch my last comment about the Teddy Bear's Picnic? If you go down to the woods today... Read on.
