Johnny5

I have heard that GR is founded upon the principle of equivalence, but I've never seen a proof of this statement, so here is my question: Is it possible to explicitly prove either of the following: 1. If GR equation is true then (priniciple of equivalence is true) 2. If (priniciple of equivalence is true) then GR equation is true. If the principle of equivalence is an assumption of GR, then that should lead to the equation, and conversely if someone understands the equation, then they should be able to derive the assumption upon which it is based. Thank you in advance

I long ago encountered a question which I have never seriously discussed with anyone at length, and I wish to do so now. Suppose that there is a way that some hollow shell object could be constructed so that Newton's third law is untrue to travellers inside of it, if the object is accelerated. For definiteness, let the object accelerate by emitting a massive amount of virtual photons. The idea is to be that the ship emits particles which follow F=ma, in the frame, but there is no reaction force on the ship. If the object starts off in space in a frame where v=0 and W=0, and then accelerates to g in that frame, and then maintains that acceleration, what would be the weight of people inside the shell? Thank you PS: Here are some links related to this topic. IOP Abstract for experimental test of Newton's third law IOP abstract discussing violations of NTL This one seems interesting Engineering Lecture It contains the following: Notice that there was talk of pushing off the vacuum. My interest in this question actually comes from problems in classical electrodynamics. In the solution of certain problems (solenoidal fields if memory serves me) in electrodynamics, there are violations of action/reaction, but I never personally understood how people were concluding that certain electromagnetic effects were demonstrating violations of Newton's third law. The reason I have focused so much on this issue, is because if Newton's third law can be violated under the right set of circumstances, then I know that the weight of the passenger in the shell will not be Mg, where M is their inertial mass, and the shell is essentially the "Einstein elevator" of the General theory of relativity, so the question is interesting on theoretical grounds alone. Mathematically, Newton's laws don't predict conservation of energy, and virtual photons depend upon violation of conservation of energy (over small amounts of time governed by the energy/time uncertainty principle... which is wishy washy). And the article above says that action/reaction can be deduced from conservation of energy, so I am not sure how all this jives with the General theory of relativity and/or the principle of equivalence. Any ideas, comments would be most welcome. Thank you

I was reading the thread entitled "photon frequency" and I now have the following question: Is photon frequency a frame dependent quantity, and if so what is the formula which discusses how f transforms? I expect to see a discussion of the Doppler effect, but I really don't know what kind of answers I will get. Suppose that the frequency of something is f0 in it's rest frame. What is its frequency in a frame in which it is moving with speed v? For example, let there be a pendulum swinging inside of a spaceship. Let the time it takes for the pendulum to go back and forth once, be amount of time T, which we can call the period of this pendulum. So this amount of time T, makes sense in the ship frame, which is a reference frame in which the center of inertia of the ship is at rest. In this frame we will define the rest frequency of the pendulum mathematically as follows: f0 = 1/T So the question is, what is the frequency of the pendulum in a reference frame in which the ships speed is v. How does frequency transform? Thanks

Are you referring to the theoretical time dilation formula?

Why can't the momentum of a photon be mv?

Disagree. Things move... so there is change of relative position of center of inertia of solid bodies. Some centers of inertia change in a regular periodic way... the center of inertia of a pendulum for example. We can use such periodic motion to construct clocks... so we have a way to measure what you call time. We didn't create 'time' to feel better. One day on earth takes 24 hours. The earth takes 365 days to move once around the sun. There are 60 minutes per hour, and sixty seconds per minute. A perfect pendulum (a perpetual motion machine) could be designed to tick once per second. Of course no perpetual motion pendulum can be constructed, because of loss of energy at the pivot point, but that's not the point. The notion of "amount of time" as something that we can measure, is wholly practical. Time isn't a physical object, time isn't material. Today physicists write equations with the letter t in them, so that they can reason about relative motion of bodies. This approach is working.

To exist means to be in the current moment in time. It is logically improper to say that "time exists" because then time is a thing inside of itself... ding an sich(thing in itself). You are obviously using the word 'exist' in some other sense, but what sense that is I have no clue. I only understand its temporal connotation. When you say "time exists" what do you mean by time? Regards

They are not joined literally' date=' mathematically they are in a certain theory, but not literally. When I say joined mathematically, I am referring to the spacetime metric of relativity: [math'] dS = \sqrt{ x^2+y^2+z^2+(ict)^2} [/math] The presence of the square root of negative one in that formula is a cause for concern. Regards

Probably If you think about it, the whole point of this thread is that the issue isn't one of probability. The original post suggests that we can infer from the current relative positions/velocity/acceleration of galaxies, that the material found there was concentrated near some single point in the past, so that we can draw the inference that probability = 1. That is the poster's whole point. That we can triangulate that position in space even now, thus properly inferring that the big bang occurred. The inference would be based upon experimental evidence, so that the truth of the premises of a short and simple argument would be empirically verifiable. I think this is a wonderful thread.

either P=1 or P=0

That is one of many theories which attempt to explain inertia, but the math is too complex for it to make sense. Calphysics ZPE

I have a question about Mach's theory of sound. I am not sure how much it influenced Albert Einstein. Mach did an analysis of some kind, and figured out that if you could ever reach the speed of sound in air, that there would be some kind of cone thing going on. From what I briefly read, the Mach equations used v/c, where v was the speed of the object in the medium, and c was the speed of sound in the medium. Einstein was a Mach fan... the v/c term, I think what Einstein did was basically apply the Mach equations to the speed of light. Einstein knew that light was a wave from Maxwell's EM theory, and for einstein the vacuum was a fluid to light, just like air is a fluid for waves. So I guess I have a few questions. 1. Who here has seen a derivation of these Mach equations? 2. What are the Mach equations? 3. What do the Mach equations predict will happen if we ever construct a plane which can reach the speed of sound? In other words, what do they predict happens when v/c=1? 4. What is the cone phenomenon which Mach figured out? 5. Do Einstein's thoughts about the speed of light in vacuum, mimic Mach's thoughts about reaching the speed of sound waves in air?

Well I wasn't talking about undeterminism, but since you bring it up... the term 'random' is highly suspect. What does it mean to say something is random? Suppose you drop an apple in earth's gravitational field, and you track the center of mass of the apple in some frame. What does undeterminism say about the path of the CM?

I can't specify what it means, that's impossible. But the following is worth mentioning: For any reasoning agent X, and any statement Y: If X knows Y then Y is true. We can know things which aren't statements, but thats not the point of the above. The point is only that if someone really does know some statement, the truth value is objective.

Yes' date=' but since it is a counterexample to your statement about statements not being true or false simultaneously, it was a good assumption on my part. I think he was killing two birds with one stone. Witty fellow, that JC.[/quote'] Let S denote J.C.'s sentence, "This statement is false." 1. S is a statement. [open scope of first assumption] 2. S is true. [open scope of second assumption] 3. S is a statement AND S is false [Meaning of S] 4. S is false. [3; simplification axiom] 5. S is true and S is false. [2,4; conjunction axiom] 6. |S|=1 and |S|=0 [better symbolic representation of 5] 7. 1=0 [6; reflexive,symmetric, transitive properties of =] 8. not(1=0) [Axiom of binary logic] 9. (1=0) and not(1=0) [7,8; conjunction axiom] 10. If S is true then (1=0) and not(1=0); close scope of 2nd assumption. 11. not (S is true) [10; Reductio ad absurdum] 12. |S|=0 or |S|=1 [Axiom of binary logic] 13. not (|S|=1) [better symbolic representation of 11] 14. |S|=0 [12,13; Disjunctive syllogism] 15. S is false [Logically equivalent English translation of 14] 16. S is a statement and S is false. [1,15; conjunction] 17. S [16; meaning of S] 18. This sentence is false. [17; S=This sentence is false] 19. |S|=1 [18] 20. |S|=0 and |S|=1 [14,19; conjunction axiom] 21. 0=1 and not(0=1) [20] 22. If S is a statement then 0=1 and not(0=1) [close scope of only remaining assumption] 23. not (S is a statement) [22; RAA] QED The correct conclusion is that S isn't a statement, therefore it does not provide a counterexample, as JC suggested. The error that is made in the Liar's paradox, is that there is a hidden assumption, namely that the sentence is a statement. Some sentences are statements, but not all. Before you begin reasoning about the sentence, you have to assume it is a statement, so even if he had written, "This sentence is false," the assumption that the sentence is a statement still has to be made by the reasoning agent first. The liar's paradox is fun though, and it does provide a reason to differentiate between sentences, and statements. This is the resolution to the liar's paradox that I use. Notice that the reasoning event terminates with the reasoner in an assumptionless state.

Are you referring to the Stern-Gerlach experiment?

No no no, that sentence won't accomplish that. Not all sentences are statements. Don't forget that. The sentence "This sentence is false" may or may not be a statement, you don't know which a priori. If you try to treat it as a statement, you will get confused, but eventually you should reach the conclusion that it isn't a statement. Either that or get bored, whichever happens to come first.

Self-referential statements... you have assumed his sentence referred to itself. Since he quoted me, I presumed he was referring to my sentence, which is my formulation of the basis of the logic I am using.

Impossible, that statement is the entire basis of first order temporal binary logic. Binary, meaning that there are exactly two truth values. Temporal meaning that some statements can have a truth value which can vary in time, though the meaning of any statement is constant in time. First order, in the sense that the universal and existential quantifiers are part of the language. An example of a statement whose truth value can vary in time is: I am hungry.

Doesn't matter if there is concensus or not. Let me have a look at 1,2,3 above... Ok that is all wrong, you introduced the binary relation 'believe' X believes Y Hintikka did that, I DO NOT EVER do that. I was only interested in statements of the form X knows Y, where X is a reasoning agent, and Y is a statement.