First of all let me say Hello! as this is my first post. I am a biologist, and have been reading over the very basics of SR for a little while and have a lot of questions on the implications of the theory. I had been asking my questions primarily at a different forum, one that wasn't directed towards physics so I figured this would be a better place for me to ask my questions and hopefully receive responses that I can comprehend. This was my last post at the forum, with a lot of the questions I had. We had previously been discussing an example of I was on an airplane traveling at 300mph, and then we talked about if I was on an airplane traveling .865c. In the first paragraph, if it is not clear, I am wanting to understand what exactly is meant by an "inertial reference frame." -- Hmm. I think the key to me understanding this is realizing what an "inertial reference frame" is. I know inertia, in the most basic sense, is an objects resistance to movement. So is the inertial reference frame the observer that isn't moving? I mean, the one that isn't traveling at speeds a fraction of c? The one on earth. I realize the person on earth is the inertial reference frame, but in the advanced calculations, since the earth is rotating around the sun, it is undergoing constant acceleration. Is this ever a factor? In addition to the above paragraph, could this be what makes us "realize" time as we do? Obviously, a second is a unit of time that we arbitrarily invented, and now it "is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. (some website from Google)". But with us rotating around the sun, it seems the sun would be the inertial reference frame (ignoring the wobble from planets) and that we on earth would be undergoing (I guess) constant acceleration. The speed of the earth around the sun is very fast, I'm sure. I'm sure over 30,000 mph. I don't have the data to do the division to see what factor of c that is, but I'm sure it's a decent factor (I'm sure less than .05c though), but much greater than the example of the airplane. Using what I've learned from you guys here and probably poor logic of my own, I would say the entire earth, and presumably everything on it has aged less than the sun (I know the sun existed before earth). Since the earth (and everything on it) is undergoing the constant acceleration, and the sun, relative to us, is static, the earth would have aged slower than the sun. Would this be a factor in calculating the age of the sun? Or is the age of the sun calculated by other means (fuel left in it)? But if any of the above has merit, then wouldn't we have to take it back a step further and look at the earth revolving around the sun, which is moving around in our galaxy? And even further, assuming a singularity-type-entity that the big bang came from, our entire galaxy is moving away from the point of the big bang at probably a very fast speed, so we'd age less than the point from which we all came from. Which I guess makes sense, that would make us younger than the universe's existence? If the Milky Way ages less than the singularity from which we came from, and, uh oh, my mind is locking up I can't see the answer here, but, oh wait no thats wrong. If it were the opposite, that would mean we've been around longer than the universe existed. Hmm. Wait, this last part about our galaxy and the singularity-type-entity we came from really isn't an issue because the singularity exploded, (I'm frowning now), and doesn't exist anymore for us to use as an inertial reference frame. But as I asked above with more complicated calculations with Einstein's SR, since all the galaxies in the universe are moving away from a central point (or each other? but couldn't you have two moving in somewhat parallel?) could the age differences be calculated using different reference frames? I'm sure they (you guys, the physicists who know this stuff) have methods for calculating the ages of galaxies, etc. Or for knowing that something is x light years away. I guess my question is if SR theory is used in addition to conventional methods, like to check for differences in ages. I guess this is also all hinged on whether or not the galaxies, our sun, the earth, etc, is moving at speeds which are large enough of a fraction of c to make a difference when calculating ages. It seems to me that even if it's a small part of c, in a time frame of 11 billion years, that it could have an effect. Even my original question/example with a 300 mph airplane would show differences over 11 billion years (although everyone would die from the airplane's disgusting food -- my apologies if anyone is an airplane food chef!) This is amazing stuff. Really, congratulations to you guys for devoting so much time to studying and understanding this stuff. Thank you anyone in advance for reading this, and for any reply you may give me. I am enjoying learning the basics of this subject. I know the time you put in a reply may seem to be worthless, but the knowledge that I and others gain is priceless. --Aychamo NOTE: I found a figure that says the earth moves about 66,000 mile per hour around the sun. That is 66,000 mi/hr / 60 min/hr / 60 sec/min = 18.33 miles per second. The speed of light is 186,000 miles/second. So the 18.33 (repeating) / 186,000 means the earth is moving at 9.85 * 10^-5c. Pretty insignificant, but still 220 times more significant than an airplane moving at 300 mph. I don't know the math, but over 4.5 billion years that is bound to have some effect. I cannot find figures for the sun's speed in revolving about in the Milky Way (I actually don't like the candy bar).
Actually inertia in terms of mass is resistence to "change in" motion. The Newtonian concept of inertia is that things unacted on by ordinary forces remain in constant motion states. In relativity it is that things unacted on by real forces, i.e. four-vector forces, remain in geodesic motion states. It isn't accelerating. The velocity one observer has with respect to another has nothing to do with whether either of them are in inertial states of motion. As long as their velocities are constants and one can neglect gravitation then both of their frames are inertial. If your worried about precision to nanoseconds in typical calculations then yes, but in the 0.865c scenarios one usually neglects such small effects. The airplane clocks weren't compared to a clock held stationary with respect to the sun, but either way the speed of the earth with respect to the sun is [tex]9.9x10^{-5}c[/tex], and [tex]\gamma[/tex] is 1.000004. Actually compared to the SR time dilation of the Earth the sun's own gravitational time dilation of its own matter is significant. These are still small effects. The big bang isn't motion of matter away from a center point within our universe. It is an expansion of space itself. There is no one single point within our universe that can be said to be the center of the explosion. The dynamics you want to consider here are general relativistic, not special at all. For example, instead of inertial frames, commoving frames are of interest. The age of the universe refers to the time elapsed for a commoving frame since big bang. When it is significant. But a comparison wasn't being made to a clock held stationary with respect to the sun.
Re: Re: SR and the earth, sun, and galaxy. I agree, but lately I've wondered if it isnt impossible to define precisely. Comoving frames differ depending on how low or high they are in gravitational potential. I used to imagine there was a universal time (since the bang) that all comoving observers could agree on, now it seems there would at best be only a rough approximate agreement. Or? Again I agree, or have gathered the same impression from reading what cosmologists have to say. The conventional scientific view is that we didnt all come from a point anywhere. The presumed spatial flatness implies that the initial singularity was infinite in spatial extent. So space was already infinite in all directions when it began expanding. the alternative view, of a finite closed universe begun at a point, has become a minority view---has become marginalized in the past 5 years or so. Maybe some time it will come back in fashion---Ned Wright had something to say about this at his website last time I looked, some tentative evidence of small positive curvature. But the majority view seems to simply be "flat or flat enough for government work". Which means an spatially infinite beginning. Do you have the same impression? ------------------------------ "Actually compared to the SR time dilation of the Earth the sun's own gravitational time dilation of its own matter is significant." that reminds me, apparently there are or were two time standards: one an imaginary clock at the center of the earth and another at the center of the sun-----no clock on the surface of the earth keeps standard time. Something about rotation. Also the atomic clocks in GPS satellites do not keep surface time but speed up and slow down along the satellites elliptical orbits as their altitudes change (among other things) so their time signals must be corrected using General Relativity (among other considerations). Strange thought, or strange to me anyway.
I've always wondered whether the CMBR could be used as a frame of reference for all observers. As the Universe expands with time, the temperature of the CMBR decreases. I suppose that wouldn't be a very practical measure of time as the CMBR wouldn't change significantly over our lifetimes. But it's just a thought. Also, our motion wrt the CMBR has been measured to be around 370 km/s. Can the CMBR be used as an absolute frame of reference with regard to motion?
Re: Re: Re: SR and the earth, sun, and galaxy. All comoving frame observers in a Robertson-Walker universe agree on this time. They are not at different "gravitational potentials". I believe it will be found to be closed curved. Right now there isn't a great weight of evidence for which side of asymtoticaly flat it actually is.
Re: Re: Re: Re: SR and the earth, sun, and galaxy. I realize that about a Robertson-Walker universe but that is where matter is spread out uniformly. And the moment you have galaxies in the universe it is no longer exactly R-W. So a comoving clock somewhere deep in Andromeda's potential-well will be ticking more slowly than a comoving clock halfway between us and Andromeda. which will be ticking more slowly than a comoving clock completely out of the Local Group altogether, not near any cluster once I raised this issue with a gravity expert (i.e. a relativist or GR person) and whether you could slice spacetime cleverly into a foliation that would define a universal time, and he gave me some arguments that you could not-----and that, if I understand what he said, the R-W universal time is just a rough approximation to an ideal which does not exist it is still a beautiful idea to be at rest with respect to the Hubble flow or, in other words, with respect to the CM Background. and that all those observers at rest wrt Background could agree down on the atomic clock age of the universe, down to the tick.
Time "Rate" FASTER on Earth than Sun! aychamo: The idea that because the Earth is moving (whatever that means), that its time "rate" , (arguing on the ideas of Special Relativity) must be slowed relative to the Sun is erroneous. The opposite is in fact the case. As a matter of fact there is "point" where a kind of "balance" occurs between the time "rate" decreasing effect of Special Relativity (SR), and the time "rate" increasing effect of "increasing" gravitational potential (ie: General Relativity, GR) as an orbit's (assume circular for simplicity) radius increases. This balance occurs at a satellite orbit (either natural or man-made satellites, the maths doesn't know any difference) altitude of half the radius of the "central attractor" (eg: this would be the Sun when considering the earth's orbit around it, or the earth, if considering an earth-tied artificial satellite). At this point the time "rate" changes of GR are exactly equal and opposite those attributable to SR. So, for example, an atomic clock in a satellite circularly orbiting the earth at half its radius (around 2,000 miles) would exhibit the same time "rate" as identical atomic clocks at the geographic poles. See: Freely Orbiting Satellites for more along these lines. (Hope you enjoy the guitar music ;-). It plays fitfully whilst it loads, at least on a slow connection, volume control at TOP of web-page, where you can also mute it when the endless repetition p**s you off too much ;-). Dennis Revell
Satellites in low earth orbit travel at 16,500mph. At that speed, time dilation in gps satellites is about 7,000 nanoseconds (seven millionths of a second) per day (and then there is the general relativity time dilation which is 45,000 nanoseconds per day in the opposite direction). That works out to about 2.5 seconds per thousand years or just over one year over the life of the universe. I got the dilation values off the net and I really hate math, so I won't try to calculate the actual values for the earth going around the sun. But it'll be within an order of magnitude or two of what I just gave you. Not real significant on the galactic timescale.
Actually russ, the formula(e) for circular orbits is(are) quite simple: The ratio of satellite time to planet or star time (actually planet/star time at its geographical poles only), for any circular orbit, is given by: GAMMA = 1/ SQRT [ 1 + GM/c²{2/R - 3/r} ] where G = Newton's Gravitational constant, M = mass of the planet/star, c = speed of light, R = planet/star radius, r = radius of orbit. If this equation hasn't already got a name, why don't I modestly call it the Revell equation. ;-) In terms of the speed v of a circularly orbiting satellite, which speed is fixed by G, M, and r, this becomes: GAMMA = 1/ SQRT [ 1 + {2h/R - 1}v²/c² ] here h = satellite altitude (ie: h = r - R). Btw, GPS satellites do not orbit at 16,500 mph. The formula relating satellite speed to altitude (for circular orbits) is quite simply, and strictly: v = SQRT [GM/(R + h)], symbols same meanings as given above, so you can work it out for any (circular) situation. Interestingly for h = 0, v² becomes GM/R, which is half of the (escape velocity)², or half of vesc², so the simplest version of expression for GAMMA becomes: GAMMA = 1/ SQRT [ 1 + {vesc²/c²}{1 - 3R/2r} ] ... unless I made a mishtake somewhere (couldn't be bothered double checking it ;-).
Hi, how are you? I am a programmer, not Physic major. I just read Physic to exercise my bored brain. I did some SR reading, but not GR yet. So, I am really a layman. I am very interested in this formula regarding time difference between two objects orbiting the same star. Is there a book that shows the derivation of this formula? Also, since the object in the Sun does not orbit the Sun, will this formula need to be adjusted to that?
Sammywu: The formula/e for circular orbits is/are given in the immediately preceding post to yours. Take your pick but version 2 or 3 are probably most appropriate. Take ver. 3: GAMMA = 1/ SQRT [ 1 + {v²esc/c²}{1 - 3R/2r} ]. If you know the escape velocity of the star (given, in case you don't, by v²esc = 2GM/R, all symbols usual meanings), then you can apply it in turn to as many orbit radii (r) as you like, the ratios will give the relative plod of time from orbit to orbit. The smaller the value of GAMMA, the more the "time-rate" of a satellite is "speeded up". Each individual GAMMA gives the time plod difference between an individual satellite and the geographical poles of the star/planet. ( and ... duh ... this is a slippery slope I'm sliding down ... ) You could even account for all (reasonably sized circular) orbits by plotting the graph of GAMMA versus r, for any given planet/star, or indeed for a completely imaginary one. ;-) Well, the proof is from General Relativity, so prepare for a long haul. ;-) The "finale" of this, as far as the information you requested is concerned, can be found as Eq. (392) from Pauli's "Theory of Relativity", Dover paperback edition: T' = T/SQRT(-g44) = T/SQRT[1 + 2Ø/c²] ... ... (392) Here Ø is the potential, and in the case you're interested in, it is the gravitational potential. For a circularly orbiting satellite you just add the centrifugal potential of -½v² to the gravitational potential to get the overall potential of (Øgrav - ½v²). and no doubt, you can find simlilar in many other places, and Einstein's original 1916 paper. But I "like" this equation, very reminiscent of the Special Relativity Lorentz Transformation. For the closest I've found to the "real McCoy", look HERE. Also see HERE for more, but I should warn you there are huge mistakes there. ;-) (I'm just waiting for a professional relativist to point them out to me. ;-) If you're not confused, you don't understand the problem.
Before I get too crazy and confused, let me propose an imaginary experiment. Let me put a space station in a remote space area far away from all gravities. Now a rocket passes by the station; at the event, you can synchronize their clocks, and we will ignite a propeller attched to the rocket pointing perpendicular to the rocket instead of parallel. This propeller will continuously generate a calculated acceleration and make the rocket go thru a circle and back to the station again at the sam speed so that we can synchronize and compare their clocks without any ambiguity again. You can see we now generate a artificial gravity on this rocket. According to the GR and SR effects you people proposed, will they exactly cancel out each other and their clocks shall match? Or does the gravity have different effect from a propeller generated artificial gravity? At the same time, I have proposed a twin paradox that could be realized without gravity and infinite acceleration, which I can not comprehend just as DR. Does this really mean that twin paradox is really meaningless? Does this click? Please help. Thanks
Another questions: Simply when applying this GR effect to some observers, there are three different kind of observers: 1. The one orbiting around the planet or sun in a circular constant speed. 2. The one free falling. 3. The one stands on the surface of the planet and supposed the planet is not spining by itself, this person actually felt two forces: the gravity that pull him down and the ground support that push him up and they cancel each other. How do their clocks tick differently? Thanks
Another experiment: You sent a rocket out of the space station that I put in the space in the previous experiment. Of course, we will give it some push for a certain amount of time until it reaches a certain speed. Let it fly for a certain time in constant speed. Then at one point, we ignite its returning propeller until it reverses its velocity ( I assume velocity is the vector one. If I am wrong, forgive the layman. ) Let it fly for a certain time and then start its bracking propeller so that it will undergo acceleration until it stops at the space station. Again we can synchronize their clocks at two events without ambiguity. Could you tell me what is their clock difference in certain formular? Keep the thought simple, you can either assume you are the clock at the station or or the clock at the rocket and give me your answer as you like. just make it clear what is T and T' in your answer.
No, the clocks won't match. Since the Rocket from its perpective is always accelerating towards the station it will perceive the station clock as running fast. The station will simply preceive the rocket clock as running slow due to its relative velocity. (The rocket's acceleration will only affect the rocket's clock in as far as it affects the rocket's relative velocity.
Janus, Thank you for your reply. Just one thing I would like to make clear. The rocket passed right by the station and retruned through the station again after a circle. The station is not in the center of the circle. Also, the station is light enough so its gravity shall be neglegible. If you still maintain your answer, where did the GR effect that proposed by other people go? It seems that only SR is making an effect here. Thank you very much. Would you might shed some lights to the other two questions?
Strictly speaking, you don't need to invoke GR for this problem, just SR as it applies to acceleration. From the perspective of the station this is simple. you only need to take into account the ship's relative velocity. From the ship's perspective, dealing with its acceleration is a bit more difficult. (The time dilation the ship measures on the station's clock will vary by not only the postion of the station with respect to the accleration but also its relative distance.) For instance, while the ship is next to the station, the acceleration of the ship is away from the station like this: <-------Ship Station. During this part of the circular path the effect seen by the ship is that the station clock runs slow both due the relative motion and the acceleration the ship experiences. since the distance between ship and station is small, the second effect will be small. During another part of the path the acceleration of the ship will point towards the station like this: Ship------->______Station The relative motion effect will be the same. But now the ship will see the station clock as running fast due to the acceleration. But now that the ship is far away from the station, this effect will be considerable. (Enough to overwhelm the relative motion effect. ) The upshot is that the rocket will measure more total time as passing on the station clock when it come back around. You really only need to invoke GR if you want to consider the spaceship as being your "at rest" frame during the whole time. Then you have to explain the motion of the station(and the force felt by the passengers of the ship as being due to a gravitational field. Then you factor in the the gravitational time dilation due to the relative postions of the ship and station in the field.
Janus, Thank you for you reply. I am still not clear. Let me make a wild guess. The GR effect seems to me is a compensation for the potential energy lost. I need to auume an observer rest at the infinite far away from the start, i.e the center of the gravity source. This observer will run a slowest clock compared with all other clocks cuaght in the vincinity of the gravity, i. e. their potential energy is negative as -GMm/R, refered as EP hereafter. Let's keep it simple for now, assuming them as rest without movement. This GR effect formulate their clock as T/sqrt(1+2EP), knowing EP as negative. This will show that the smaller is R, the higher is the T. Now lets assume the object in vincinity is moving, then all we need to do is add the SR effect, which is oppsite to the GR figure in sign, back to the object. If this is correct, we then equate the clock in the infinitely far away to the center of the gravity source. Here is what bother me. How could you simply equate a clock so far to the clock in the gravity center? Do i do it right? If it's complete baloney, please let me know. If I capture it, please correct me any place I am wrong. Now, If it somehow captures our mainstream scientist, I will ask another question. Back to the mass-energy equation, my impresion is the mass is really how an outsider measure the internal dynamic of an enclosed confinement ( simply said, box ). Einstein has shown how to derive the mass of photon in the way in SR. Now, gravity potential energy, actually all potential energy, bother me. If I can confine two masses, M and m, and keep them in a certain distance inside that confiement, what will be the mass when we measure it. Could it be M+m-GMm/Rc**2? Thanks