Lethe, No, not really. For example I see GR as being generally valid but for the wrong reasons as presented. That is the issue of "Curved Space" to me is absolutely valid but is better shown as a function of the origin of gravitational force (energy flow and attenutation) and space being a function of energy density, naturally causes distance to be variable as a function of the masses of the observer and observed. The result are the same but one has cause and greter implications for the universe and reality, the other doesn't. http://www.sciforums.com/attachment.php?attachmentid=2696 http://www.sciforums.com/attachment.php?attachmentid=2697 "Move your mouse to the speck in the upper left corner until the enlarge button appears then click it." Note how I have avoided the terriable "U" word. Please Register or Log in to view the hidden image!
GR is usually presented as the logical result of the equivalence principle. do you think the equivalence principle is wrong? OK, great, so you like curved space. me too. i am fearful to ask what you think the implications of these two alternate views for the universe are.
Lethe, Not at all. I see why there is an equivelence principle. Absolutely, but have you ever realized what that actually means? That is that distance is not the same between objects for different observers at rest? For purposes of this string I'll let the above comment stand as the answer here - although there is much more. If you don't follow the variable distance arguement then read the segment in the two links about the issue.Please Register or Log in to view the hidden image!
enlarge button? i have no idea what you are talking about. probably i have a different sort of computer than you, and it doesn't have an enlarge button. and i see nothing in those diagrams.
OK, so then what is wrong about the reasons in GR as it is usually presented? bear in mind that GR is usually presented as the logical conclusion of the equivalence principle. well... this is already true in special relativity. what happens in curved space is that, for example, the sum of the angles of a triangle is not 180 degrees.
lethe, If you see nothing then look very carefully to the upper left corner. You should see a speck. Even if you can't see it move your mouse about x,y = 1 inch from the upper left corner. You should see an oragne square appear at the lower area of your screen. click on it. Gotta go cut some trees. Back later.
Lethe, I would have to say the inertia of mass and gravity equivelence principle are indeed a function of the same physics. I'm not convienced that GR mathematics is the proper description of those functions. Not talking about angles of a triangle. I'm asking if you ever had thought that if a Bowling Ball and a Golf Ball were setting side by side and a Ping Pong Ball is some distance away on a line perpenticular and in the center of the line between those balls centers, forming an Isosceles triangle between centers of the three balls, that GR would mean that the length of the two sides of the isosceles triangle are not the same.! I know that defies the description of an isosceles triangle but that is another matter because it is only an illusion from our perspective that those sides would be equal. In reality it is not an isosceles triangle.
ryans, HeHeHe. Please Register or Log in to view the hidden image! Back for more I see. I would think you would rather leave that subject alone. Your statement is valid only for properly defined conditions, which you were all wet on and I was correct where that issue was debated.
If you can accept that the internal angles of a triangle do not sum to 180 degrees in curved space, then surely you can use the same model to see that the relevant ration does not equal Pi? P.S. Let's be civilised shall we, so that means no name calling or superlfuous internet references.
Ryans, As I said the Pi ratio is only applicable under properly defined circumstances. I have never said relavistically the ratio doesn't change. You'll find I hold no grudge and will be as civilized as those that interact with me. I do question your description of a Physicist's reply as being superfluous however.
I'm surprised that you had so many problems getting an answer. The answer to your question is Yes. If a body is moving then the gravitational field generated by the moving body is stronger. Recall what Einstein stated in his 1916 paper The Foundation of the General Theory of Relativity The tensor he speaks of is the stress-energy-momentum tensor T^uv. The T^00 component is defined as T^00 = c^2(mass density). For this reason it is said that mass is the source of gravity. For more on this see Cosmological Principles, John A. Peacock, Cambridge University Press, (1999) page 17-18 http://assets.cambridge.org/0521422701/sample/0521422701WS.pdf The complete description of mass is a tensor. This tensor you could call the mass-momentum tensor. But whatever name you give it its just proportional to T^uv. There is no real reason to say that one tensor is the source while the other tensor is not. I.e. I can defined M^uv as M^uv = T^uv/c^2 where M^00 = mass density Einstein's field equations could then expressed as H = (4*pi/c^2)M where H = (c^2/2)G where G is the Einstein tensor. Which one used is a matter of taste. Regarding mass as the source of gravity. Well if I were to quote "Gravitation," by Misner, Thorne and Wheeler - "Mass is the source of gravityt." This is similar to saying that charge is the source of the elecctromagnetic field. The complete description of charge is the 4-current J^u where J^0 = c*(charge density). The difference being that mass is a function of speed where as charged is not. If you had a box of particles, e.g. a gas, then if the kinetic energy of the particles is large enough, i.e. you keep pumping in more and more energy making the particles move faster and faster and the kinetic energy becoming higher and higher, then eventually the box would turn into a black hole (assuming the walls of the box didn't collapse). This, however, does not mean that a baseball in one frame turns into a black hole in another frame. One requires only that the energy of the gas with a finite space have a certain value. I could have just as well taken the same amount of mass and placed it in a small enough space and it would be a black hole. An object is not a black hole because it has a certain amount of mass. It's a black hole because its mass is confined to a certain region of space. I.e. all its mass is confined within a sphere whose radius is the Scwarzschild radius. Yes. Photons generate a gravitational field. They have momentum and anything with momentum has (relativistic) mass. Note: A moving particle weighs more than the same particle at rest. Yes - photons produce their own gravitational field. I do not believe that photons moving parallel to not attract each other. I do believe that if they're traveling antiparallel that they do attract each other. Note - Some people like to use the term "mass" to refer only to proper mass because they hold that the term "relativistic mass" leads to errors. That is 100% incorrect. A person may make errors but that is only due to a misunderstanding they have with relativity. Trying to avoid this by speaking only in terms or rest masss servers only to trade one set of errors for another set of errors. E.g. Some people make the mistake of thinking that a moving object will become a black hole if if its moving fast enough. For reasons like this some people say "Don't think of mass as relativistic mass. Think only in terms or rest mass." Then what happens is that some people then say "Oh! So mass is rest mass. Then since the rest mass of light is zero it follows that a directed beam of light has no gravitational field!" - What has happened is that one set of misunderstandings has been traded for another set of misunderstandings. The most reasonable thing that can carry the name mass is relativistic mass.
What relativity says about the appearance of life and mind. I don't see why one should take so seriously incomplete description of reality. photons should have some subtance and therefore mass. it is a matter of math description how we shell treat their small mass.
pmb, Interesting. Your profile doesn't show your qualifications, so we'll have to read between the lines. You have made an absolute statement and seem to make light that not everyone seems to hold your view. Yes, he specifically warned about not considering relavistic mass but momentum. However, it is somwhat difficult to visualize how infinite momentum can occur in absence of infinite velocity or infinite mass. It seems a bit more of sweep it under the rug than a clear answer. True it isn't mass but mass density that creates a Black Hole. There are infact known to be microscopic Black Holes. Infact many labs are experimenting at trying to make such Black Holes. But your response seems to indicate you are aware that there are other views than the one your advanced as being the only correct view. What is your basis to claim your view is correct and the others aren't. OK, I'll accept that noting that this infers that mass/gravity causes light to bend passing near the sun and not curved space. OK, so you are saying relavistic mass is real. Einstein said don't consider that. Interesting idea but it seems a bit confusing to think that a photon can have different gravity (hence move differently) to different observers. Can you qualify this a bit? Interesting how you taut Einstein in one area and then oppose him in another. Eistein said do not consider relavistic mass.
I don't see that I made light of anything. To me its simply a matter of opinion. Regarding qualifications - I'll give them to anyone whom I wish to work for. But on forums I'm just interesting in discussing physics I don't see where that matters. If one wishes me to back up a statement then I'll do so. If someone wants me to derive something which I stated/claimed I'll be glad to do so. If someone is really that interested in what my qualifications are then I'll be happy to tell them - in e-mail of course (see e-mail address below). But I'll give you a few hints - I'm the "Peter M. Brown" in the following http://www.whoi.edu/science/PO/people/jprice/class/aCt.pdf http://www.eftaylor.com/pub/front_matter.pdf http://cosmo.fis.fc.ul.pt/~Fisica2002/TaylorEvora.pdf http://arxiv.org/pdf/physics/0204044 http://arxiv.org/pdf/physics/0308039 Regarding "absolute statement". If you mean the fact that the strength of the gravitational field is frame dependant then that is certainly not a matter of opinion. That is a matter of fact. As an example see the article "Measuring the active gravitational mass of a moving object," D. W. Olson and R. C. Guarino, Am. J. Phys., Am. J. Phys. 53, 661 (1985). The abstract reads I can e-mail this to anyone who wishes to read it. There are other examples too. I've worked out another one on my web page. http://www.geocities.com/physics_world/gr/grav_moving_rod.htm I'm working on another one but the physics is the same. The only difference being the gravitaitonal potential is a different function. Actually that is not quite true. Einstein never really warned about relativistic mass per se. Einstein said that it is not good to introduce m = gamma*m_o*v Relativistic mass is defined as the m in p = mv. This is the spatial component of a particle's 4-momentum P. For a tardyon (I.e. v < c and thus m_o > 0) its given by P^k = p^k = mv^k where m = m_o*dt/dT where T is proper time. E.g. If the metric is time orthogonal (i.e. g_0k = 0) then dt/dT = 1/sqrt[1 + 2*Phi/c^2 - beta^2] where Phi = (g_oo - 1)c^2/2 For v << c dt/dT ~ 1/sqrt[1 + 2*Phi/c^2] M ~ m_o/sqrt[1 + 2*Phi/c^2] Thus for a slowly moving particle the mass is still dependant on the gravitational potential - At least, that is, according to Einstein. But I do agree with him on this point. When it came to radiation Einstein did state that electromagnetic energy has a mass densit rho which was related to its energy density u by rho = u/c^2. This still is used today by many cosmologists, e.g. Peacock, etc. Consider how Alan Guth explains all this in his class notes from his "Early Universe" course at MIT http://www.geocities.com/physics_world/guth.gif I'm afraid you misread. Nowhere did I state that this was the only correct view. I made two points (1) When you try to switch from relativistic mass to rest mass for because you think relativistic mass is the source of a few errors made by students just learning relativity then all you're doing is giving them a definition which has lead to other misunderstandings. (2) I believe that mass = relativistic mass is the most reasonable way to define the term "mass" since it has all the properties associated with mass and it fits more naturally into relativity. I do not believe that the notion of proper mass is not useful. Consider the two types of "time" and distance that is used in relativity. There is "time" and there is "proper time." E.g. Consider the timelike spacetime displacement dX where dX = (cdt, dr) dt = time interval, dr = spatial displacement. Then the proper time interval, dT, is given by c^2*dT^2 = |dX|^2 Likewise there is "distance" L and there is "proper distance" q. Consider the spacelike spacetime interval dX = (cdt, dr). Then dq^ = -|dX|^2 In a similar fashion there is "mass" m and "proper mass", m_o where. Consider the 4-momentum P = (cm, p) c^2*(m_o)^2 = |P|^2 There is a nice pattern here. Think of proper mass as you would all other proper quantities and think of mass as one of the components of the 4-vector of which proper mass is the magnitude of. The idea of proper mass cannot be extended to something more general in relativity. For example: In SR one cannot, in general, define a proper mass for an arbitrary system of particles. This is only possible for a closed system of particles. To be detailed in this would take up far too much room here. In fact when I tried to write it up to be complete and precise it took 84 pages. However if anyone wishes to read it then feel free to e-mail me at peter.brown46@verizon.net Not really. He refered to a specific case. And he seemed only to be refering to special relativity. He made such a comment in a letter to Lincoln Barnett in 1948. There was an article about all this in Physics Today back in 1989 by Lev Okun. I assume that's what you're refering to. If so then Okun was unaware of something else in Einstein's book that he was quoting. He took one part of his book (as well as a letter to Linbcoln Barnettr) as proof of his idea that Einstein didn't like relativistic mass but he ignored the GR section of Einstein's text where Einstein actually used it. In his relativity text "The Meaning of Relativity" where he addresses both SR and GR he didn't follow that rule when it came to mass in GR. In fact Einstein himself stated that inertial mass of a body depends on the gravitational potential of the body. And the last revision he made to that text was in the mid 50's (1954). Had he changed his mind and wanted to use the term "mass" to only refer to proper mass then his idea of Mach's Principle wouhld have been meaningless. He also said indicated that light has mass in his text "The Evolution of Physics" (I'm too lazy to look it up right now - will upon request) A problem was worked out regarding this way back in 1931 in the paper "On The Gravitational Field Produced by Light," Tolman, Ehrenfest and Podolsky, Physical Review, Vol(37), March 1, 1931, pg 602-615 Tolman works this out in his text "Relativity, Thermodynamics and Cosmology," Richard C. Tolman, Dover Pub, Sections 112-115 cover more aspects of the gravitational field generated by light than is presented here. See - http://www.geocities.com/physics_world/grav_light.htm Interesting how you taut Einstein in one area and then oppose him in another. Eistein said do not consider relavistic mass.[/QUOTE] It would be weird for me to agree with every single view point by any single individual. But in this case I believe I'm justified since it appears to me that Einstein had a different definition of mass for different applications. that doesn't seem like a reasonable thing to do. But I only disagree with his notion about the velocity depedance regarding the mass of a tardyon. In other aapplications where Einstein used the idea I agree with him. Pete
pmb, Perhaps I misread your tone but it seemed the comment about "I don't see why it took so long......(and then gave your answer as though yours might be the only correct view. It is not necessary to give qualifications but it would certainly help others determine how much weight to give your views. OK, suppose I agree that it is a matter of fact, then we should be able to answer this simple fact. If I assume the earth orbits the sun or the moon orbits the earth in a balance between gravity per Fg = m1*m2/r^2 and centrifugal force Fc = m*v^2/r, I find I have a unique situation. If I assume I am in a rocket with a relative velocity to the earth and moon and I fly over the orbital plane and inbetween the earth and moon at 86.6% c, then I should see m1 and m2 double. Fg therefore becomes 2 * 2 = 4 times the gravity. But the counter balancing centrifugal force of the moon Fc = 2. You have quadroupled the gravity but only doubled the centrifugal force. So why doesn't the moon spiral down to earth when we fly by? If that isn't bad enough, if you have two bowling balls moving (initially parallel) in space they will gradually be drawn together by the Fg calculation above. Depending on the seperation there is a given amount of time before they collide. Yet there can be an umlimited number of observers flying around out there watching the experiment, all at different velocities, and each observer would find that the bowling balls aren't obeying the laws of physics since they can only close at their rest mass rate for gravity. Otherwise there would have to be numerous different times before collision. Show us how your view resolves these issues. Actually Einstein's point of view is described in the following quote: "It is not good to introduce the concept of the mass of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the 'rest mass' m. Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion." Go to: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relcon.html#relcon Then Click on "Relavistic Mass" Then Click on "Problems with Relavistic Mass" at the bottom of that block.
Thanks for this explanation. How do you know that the rest mass increases with higher transverse inertia? I understand this. I still don't understand why the moving ball (or grain of sand) outside of the box does not have a stronger gravitational attraction than a stationary ball or grain. (It seems that pmb says that it should.) If the grain of sand hits the sun at sufficiently close to c the sun will be destroyed as we know it, due to the grain's energy of momentum, which can approach infinity. Why wouldn't that energy be reflected by a stronger gravitational field such that the grain, if it grazed the sun, could damage the sun?
Why? Note that in the spring analogy, the total energy is the same... just alternating between spring potential energy and particle kinetic energy. In the spring analogy, there is obviously real energy in the system when the spring is stretched... but what about when the spring is relaxed? How is that different to an unconfined particle at that instant? The difficulty is that gravity is not frame-dependant, but relativistic mass is. I don't know how pmb accounts for this. Consider things from the grain of sand's reference frame. In the grain's reference frame, the grain is stationary, and the Sun is moving very very fast. The Sun's relativistic mass is enormous... So much that it should collapse into a Black Hole. It doesn't, of course. Relativistic mass obviously does not directly produce a gravitational field. I have a potentially crackpot idea that while kinetic energy does not produce a gravitational field, a change in momentum does produce a gravity wave. For the confined particle, it is changing momentum with every collision with the box walls... and the cumulative gravity waves look like a gravitational field that matches the particle's kinetic energy. I don't think this has far-reaching implications... it's just interesting.
I wrote that because I looked through the posts and I didn't see a direct response to the question asked. That was all I meant. However there were a ton of responses so I didn't read them all and there probably was an answer. Regarding "view" - I don't believe that I posted anything which constitutes a different view beyong a difference of opinion on how a term should be defined. How a term should be defined as merely a matter of opinion and I see no way in which any claim that a definition is wrong can be correct. I agree that this is a valid point. I'm a physicist. I've spent about 15 years learning SR beyond college and 5 years studying GR. Ahh! Excellent question. This is why I love these discussion forums. I'll take a crack at an answer: A question may sound easy and yet may be difficult to provide a precise answer. Perhaps an answer by analogy. You're ignoring gravitational radiation. So let's consider the similar situation in EM and ignore EM radiation. If I ignore EM radiation then we can have a stable orbit of a negative charge orbiting a positive charge. Then the centifugal force is counter balanced by the electric force. Assume the mass of the positive charge is so massive that we can basically consider it to be at rest (i.e. we ignore its acceleration). Let S be the rest frame of the positive charge. Change frames from S to S' where S is in standard configuration with S'. In the new frame there is a magnetic field. The electric field has also changed. The component of the E field parallel to the velocity of S relative to S' will remain unchanged. The component of the field perpendicular to the field will increase by a factor of gamma. However in this new frame there is also a magnetic field which has a transverse component equal to (v/c)xE where E is the electric field and v is the velocity of the frame. In relativity all forces are velocity dependant and this is no different in GR since the gravitational force is also velocity dependant. In GR there is a paradigm in called "gravitomagnetism". This paradigm views the the equations of motion etc. in the weak field approximation in terms of equations which are nearly identical to Maxewell's equations. Regarding the gravitational case that you mention - In the new frame S there is an increased gravitomelectric field but now there a gravitomagnetic field. If you can understand why the negative charge can orbit the positive charge in each frame then you should now be able to understand why the moon can orbit the Earth in the new frame. I can go ahead and try to do a calculation in the EM case and find where each component is increasing and decreasing and where each component is comming into play in the EM case etc. But I imagine you're able to do that yourself. We can go over this if you'd like? I disagree. The rate at which they approach each other is frame dependant due to time dilation. Consider the same question with a positive and negative charge and how fast they approach each other. [quote Actually Einstein's point of view is described in the following quote: "It is not good to introduce the concept of the mass of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the 'rest mass' m. Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion." Go to: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relcon.html#relcon [/quote] Thanks. I'm intimately familiar with Einstein's thoughts on this matter. In fact his comment is why I chose to study the concept of mass in detail. In fact I have a copy of Einstein's letter. I even had to send away to Isael to get it. Yes. As I agreed earlier Einstein said that a mass should not be given which is veclocity dependant. But he did not say that relativistic mass was a bad idea. It may seem that he did because many people actually define M(v) = m/sqrt[1-v^2/c^2] as the definition of relativistic mass. However that is quite untrue. That is a result of the choice of defining mass as relativistic mass. Another result is that light has mass and Eisntein agreed that light has mass. Einstein never really disagreed with the definition of relativistic mass as it is defined today, i.e. as the ratio of momentum to velocity. Since light momentum it has energy. One can also say that since light has energy it has mass. This is why I say that Einstein never disagreed with the defintion of relativistic mass. Taken in a vacuum that comment of Einstein's seems to support the claim that Einstein held that relativistic mass was a bad idea. As such it seems almost a matter of fact that Einstein would say that light does not have mass or that a body's mass can't change when placed in a gravitational field. However the contrary is true. Einstein also wrote that light has mass since it has energy. In his and Infeld’s book The Evolution of Physics dated 1938, Einstein comments on the observation made by an observer inside an accelerating elevator. The elevator observer claims that light is ‘weightless’. Einstein then explains on page 31 Now consider what Einstein states in his GR book, the last edition of which was dated after his comment in that letter. Note that this was Einstein's most rigorous book on relativity You mention a page which claims there are problems with relativistic mass. There are no problems other than students have a difficult understanding relativity. Note what that page argues (1) You can use relativsitic mass to explain particle motion in accelerators (2) Einstein seemed to say that he didn't like it (3) You don't need it. Regarding point 2 - It only seemed that Eintein didn't like relativsitic mass. In actuality he was inconsistent with his use of the term mass. Sometimes he used the concept and at other times he didn't. Regarding point 3 - That's not a meaningful statement. It pretends that relativitic mass doesn't exist when in fact you're just not naming it. For example: The Lorentz force is given by d(gamma*m*v)/dt = q(E + vxB) where m = proper mass. Notice how the letter "p" doesn't appear in that equation? Notice how the letter "f" doesn't appear in that equation? Does this mean that I don't need or use the concept of force or momentum?
Gravity is frame-dependant. In fact the very existance of a gravitational field is frame-dependant (although the existance of tidal forces is not) as Einstein himself said. From "The Foundation of the General Theory of Relativity," by Albert Einstein (1916) (Annalen der Physik 49) This is probably the most famous result of general relativity. I worked out an example here for the case of a long (infinite) rod (I posted the wrong link before - sorry) http://www.geocities.com/physics_world/gr/grav_moving_rod.htm See Eq. (27) in that link. It shows that the z-component of the gravitational acceleration is given by du_x/dt = - 2mG*gamma^2(1+beta^2_)L_o/z where gamma = 1/sqrt[1-v^2/c^2) where v = velocity of rod and L_o = proper mass density of the rod. The relativistic mass density is given by L = gamma*L_o One factor is for mass increase and one factor of gamma is for volume decrease. So I can write the above as dp_x/dt = - 2mG*(1+beta^2_)L/z Therefore the intensity of the gravitational field is a function of the speed of the source An object like the sun is not a black hole, not because its mass is not large enough. It's not a black hole becuase its mass-energy is not confined to within certain region of space i.e. the mass of the sun is not contained within a sphere whose radius is the Scwarzchild radius. For example: Hawking postulated the existance of micro black holes. These have a mass on the order of magnitude of the mass of Mount Everest. However Mount Everest is not a black hole. Think of EM - Even there charge is not a function of speed however its well know that the intensity of the electric field is a function of the speed of the source. In some situations one can think of the increase in the magnitude of the E field as being due to an increase in the charge density. A sheet of charge is a great example. If you worked out the electric field in the rest frame and the moving frame in detail then you'd see why this is so. In the moving frame the charge density has increased. Since the electric field of a sheet of mass is proportional to the charge density of the sheet then it follows that if the charge density increases so too with the electric field. Since volume decreases with speed the charge density will increase and so too with the magnitude of the electric field. However there is now an magnetic field. The force of the magnetic field can be ignored if you set the velocity of the charge to be zero. The force is then entirely electric. In SR charge is the source of the EM field. But one can think of it as charge in one frame is charge and current in another frame. Its a well known fact that relativistic mass is the source of gravity. For an example of such a statement in the GR literature this can be found in "Gravitation," by Misner, Thorne and Wheeler, on page 404. What we call "relativistic mass" they call "Mass" or "mass-energy". However this is a fine point which is a source of debate. Similarly, in GR mass, momentum and stress are sources of gravity. You can think of relativistic mass as gravitational charge and you can think as momentum as an electric current. In fact this is what one does in gravitomagnetism. That's why the strength of the gravitational field increases with speed. For the sun to become a black hole you have to compress it into a sphere whose radius is smaller that the Schwarzschild radius of the Sun's mass. To give you a touchy feely explanation of this consider the fact that the diameter of a sphere will contract with velocity. Consider two spheres A and B which are at rest in frame S. If sphere A is larger than sphere B in its rest frame then sphere A will not fit inside sphere B. Change to the moving frame S'. The sphere's will be compressed into ellipsoids since lenghts parallel to the motion are contracted. Sphere A becomes ellipsoid A and sphere B becomes ellipsoid B. Ellipsoid B will not fit inside ellipsoid A regardless of the speed of the frame. Why do you think kinetic energy does not contribute to the strength of the gravitational field? See "Kinetic Energy and the Equivalence Principle," Steve Carlip, Am.J.Phys. 65 (1998) 409-413. Abstract reads This is available online at http://xxx.lanl.gov/abs/gr-qc/9909014
