Ifmdeng said:Thanks for the math. Regarding the deductions, does the final result hold for v1 = -v2? It would make the denominator equal 0.tangh\ R\ =\ \frac{v_1/c+v_2/c}{1+v_1v_2/c^2}\ =\ \frac{tangh\ R_1+tangh\ R_2}{1+tangh\ R_1\ tangh\ R_2}\ =\ tangh(R_1+R_2)
lightarrow said:If
v_1 = -v_2
the denominator is not zero but
1 - v_1^2/c^2.
thus can’t be explained by the principle of relativity.
As you noted in other posts the more scientific question is "how". Science answers "how" questions much better than "why" questions. However, that was not what I was referring to in this case.mdeng said:I hope/think you are not referring to the question of mine about why light has a constant speed c to anyone and everyone.
If you refuse to allow experimental evidence in the answer then you are rejecting the scientific method and therefore you are not asking a scientific question. In fact, your question of this thread appears to be a philosophical or mathematical question.mdeng said:Well, it's not a proof, is it? "Proof by example" is not a proof
I tend to agree with you on this point. I have often thought that the first postulate was sufficient and that the second postulate is simply a corolary to the first one. But I have been told by rather reliable sources that I was wrong, they were actually two separate postulates, and I didn't feel strongly enough about it to argue. I have a similar "wrong but not strong" opinion about Newton's first and second laws.rbj said:i fail to see how mdeng can accept the broader postulate of relativity, that "any law of nature should be the same at all times; and scientific investigations generally assume that laws of nature are the same regardless of the person measuring them", yet insist that a quantitative parameter of some of those laws can vary and, for some reason, needs yet another postulate to tie it down to a fixed value (at least between inertial observers). i don't get it, and i doubt that mdeng will convince me that I'm the one that's missing something in the logic here.
DaleSpam said:As you noted in other posts the more scientific question is "how". Science answers "how" questions much better than "why" questions. However, that was not what I was referring to in this case.
DaleSpam said:What I am talking about is this:If you refuse to allow experimental evidence in the answer then you are rejecting the scientific method and therefore you are not asking a scientific question. In fact, your question of this thread appears to be a philosophical or mathematical question.
DaleSpam said:I tend to agree with you on this point. I have often thought that the first postulate was sufficient and that the second postulate is simply a corolary to the first one. But I have been told by rather reliable sources that I was wrong, they were actually two separate postulates, and I didn't feel strongly enough about it to argue. I have a similar "wrong but not strong" opinion about Newton's first and second laws.
phyti said:If the theory is based on the first and second postulates, then the speed of light 'c' is guaranteed, but the abstract mathematical manipulations will not reveal the 'how' or 'why'. The purpose of the theory is to produce numbers that agree with measurements/perceptions by the observer. To explain 'why', you have to analyze the behaviour in terms of physical processes. There is an answer to this, just as there is for time dilation.
DaleSpam said:I tend to agree with you on this point. I have often thought that the first postulate was sufficient and that the second postulate is simply a corolary to the first one.
I have a similar "wrong but not strong" opinion about Newton's first and second laws.
In that case R itself is not defined because artgh(1) is not defined.mdeng said:I meant v_1=-v_2 and |v_1| = c. I guess it still holds.
mdeng said:What is the physics answer to the question of why light has an invariant speed
to anyone and everyone, other than this is what light is? There must be a
reason why light behaves this way (or perhaps not necessarily this way
always). I'd think something must have happened external to the light to give
it this peculiar property. Put it in another way, what's wrong with the
classical physics where velocity would follow the law of vector arithmetics,
when applied to light?
Thanks,
- Ming
You can solve the problem too.Einstein lifted the idea that the speed of light is constant intact from electromagnetic theory, devised forty years earlier by the Scottish-born physicist James Clerk Maxwell. Part of Einstein's larger ambition was to reconcile electromagnetism with Galilean relativity. Then one night in May 1905, after discussing the problem with his longtime friend Michele Besso, Einstein saw how to do so.
Thank you!" Einstein greeted Besso the following morning. I have completely solved the problem."
The solution, he explained, lay in a reconception of the idea of time. Any velocity is simply distance divided by time. In the case of light, though, the velocity isn't just 186,282 miles per second; according to Einstein's postulate, it's always 186,282 miles per second. It's a constant. It's on one side of the equal sign, humming along at its imperturbable rate. On the other side of the equal sign are distance and time, which become, by default, variables. They can undergo as many changes in value as you can imagine, as long as they continue to divide in such a way that the result is 186,282 miles per second. Change the distance, and you have to change the time.
belliott4488 said:I would say that historically we first discovered that the speed of light is invariant and then from that learned the properties of space and time (as described by Special Relativity). Now that we know those properties, however, I would venture to say that it is a property of space and time that massless particles always move at the maximum speed that any object can obtain, which is also invariant for different observers. Light happens to be an example but is otherwise not special.
In other words, I'd say the invariance of the speed of light is a by-product of the underlying properties of space-time, so the question becomes, why are space and time the way they are? I doubt there's a definitive answer for that yet.
Don't confuse how we deduce the consequences of relativity from the usual postulates with how we interpret "why" things are the way they are. I'd agree with belliott4488 that it's space and time itself that is structured in such a way as to make anything moving with speed c have an invariant speed with respect to any frame. It's interesting that light has such a property, but not fundamental.Xeinstein said:I disagree.
I'd say the underlying properties of space-time is a by-product of the invariance of the speed of light which is a postulate of SR
Doc Al said:Don't confuse how we deduce the consequences of relativity from the usual postulates with how we interpret "why" things are the way they are. I'd agree with belliott4488 that it's space and time itself that is structured in such a way as to make anything moving with speed c have an invariant speed with respect to any frame. It's interesting that light has such a property, but not fundamental.
Doc Al said:Don't confuse how we deduce the consequences of relativity from the usual postulates with how we interpret "why" things are the way they are. I'd agree with belliott4488 that it's space and time itself that is structured in such a way as to make anything moving with speed c have an invariant speed with respect to any frame. It's interesting that light has such a property, but not fundamental.
I agree with you. Light doesn't just "happen" to have a speed equal to the apparent "speed limit" of the universe. Something more fundamental is going on.rbj said:Doc, i think that it is fundamental (perhaps not yet verified experimentally) that any of these fundamental interactions, EM, gravity, weak, strong, all ostensibly "instantaneous", are all believed to have a delayed effect on a distant object when viewed by an observer that is equi-distant from the source of the action and the object affected by the action. it's not that light just happens to propagate at a speed of c. it's that light is EM and EM is one of these fundamental interactions and all of these fundamental interactions have effect that propagate at the same finite speed.
mdeng said:Another question I had, as posted in the Quantum group, what happens to non-photon particles that are moving at a speed close to c and are moving against each other? Is the relative speed of the two particle beams (whose sum is > c) capped by c? Relativity theory says yes. But what would be the mechanics behind this phenomenon? And would this be called "invarance of upbound of relative speed"?
It's worth distinguishing two types of "relative motion" here. In the frame where both particles are moving in opposite directions, each one is moving at less than c, but the distance between them can increase at a rate greater than 1 light-year per year. But in each particle's own rest frame, using rulers and clocks at rest in that frame to measure the distance covered by the other particle in a given time, the other particle's speed in this frame will be less than c.Xeinstein said:Two particles moving at .999c and -999c relative to one observer still see a relative speed less than c in their own frames.mdeng said:Another question I had, as posted in the Quantum group, what happens to non-photon particles that are moving at a speed close to c and are moving against each other? Is the relative speed of the two particle beams (whose sum is > c) capped by c? Relativity theory says yes. But what would be the mechanics behind this phenomenon? And would this be called "invarance of upbound of relative speed"?
Yes, the relative speed of the two particle beams (whose sum is > c) capped by c.
This is a result of time dilation. The faster you travel in space, the slower you travel in time. Nevertheless, the length of 4-velocity of any inertial observer is always c
Doc Al said:I agree with you. Light doesn't just "happen" to have a speed equal to the apparent "speed limit" of the universe. Something more fundamental is going on. My point was that relativity itself is more fundamental than just a strange consequence of the behavior of light.
Why do you think nature had little other choice? There doesn't seem to be anything inherently inconsistent about the Newtonian universe which allows arbitrarily large velocities.rbj said:so it's not just c that is invariant. and, if i understand Einstein's sentiment correctly, Nature had little other choice. i don't know how he would have taken it if the M-M experiment came out differently than it had.
rbj said:so it's not just c that is invariant. and, if i understand Einstein's sentiment correctly, Nature had little other choice. i don't know how he would have taken it if the M-M experiment came out differently than it had.
JesseM said:Why do you think nature had little other choice? There doesn't seem to be anything inherently inconsistent about the Newtonian universe which allows arbitrarily large velocities.
All I have tried to do in my life is ask a few questions. Could God have created the universe in any other way, or had he no choice? And how would I have made the universe if I had the chance?
I believe in Spinoza's God, who reveals Himself in the lawful harmony of the world, not in a God Who concerns Himself with the fate and the doings of mankind...I do not believe in a personal God and I have never denied this but have expressed it clearly.
mdeng said:I think the argument of "[a universe where] the laws of nature were different for two inertial observers was a universe that did not make sense [to Einstein]" is strong (as it fits what we observed, but remember Newtonian laws were also observed as fits for hundreds of years). However, RBJ's earlier argument assumed that this was sufficient to derive SR. I am glad RBJ adds back the constancy of C to the postulate.
I am very curiously though, why without it Einstein's SR would fall apart even though he already had Maxwell's equation? In other words, what's wrong to replace Einstein's 2nd postulate with Maxwell's conclusion of C (which is a theory, not a postulate, though I am not sure what Maxwell's postulate was)?
rbj said:be careful how you represent what other people say (or type). i haven't changed my position. the constancy of c (for various inertial observers) is because of the constancy of the laws of nature (for the same inertial observers).
What I meant to say is, why did Einstein have to make the 2nd postulate. All he seemed to have to do was to argue that Maxwell's equation must be true for all inertia systems (I think that was your line of arguments earlier). I believe he could not do that. But I don't truly understand why he could not. IOW, why would he be wrong if he did not have his 2nd postulate?rbj said:i didn't think that Maxwell concluded that c was constant for different inertial observers. if he did, i would like to know of the record of that. i thought that Maxwell (as well as Faraday) understood that c was in reference with the aether. what Maxwell concluded was that
c = \sqrt{\frac{1}{\epsilon_0 \mu_0}}
mdeng said:What I meant to say is, why did Einstein have to make the 2nd postulate? All he seemed to have to do was to argue that Maxwell's equation must be true for all inertia systems (I think that was your line of arguments earlier). I believe he could not do that. But I don't truly understand why he could not. IOW, why would he be wrong if he did not have his 2nd postulate?
With quantum field theory I think this is true, but back when the only law of nature involving c was Maxwell's laws, couldn't one have argued that Maxwell's laws are not really fundamental, but just a description of the behavior of a certain physical medium filling space (the aether)? After all, no one says that since observers at rest relative to the atmosphere measure sound waves in air to have the same speed in all directions, then this must imply by the first postulate that sound waves in air must have the same speed in all directions in every frame (even in a universe where all of space was filled by such an atmosphere).rbj said:well, you're basically proving my point. i think the 2nd postulate was there for clarity and was not strictly needed. acceptance of the 1st postulate forces one to accept the 2nd. there is no way for the laws of nature to be precisely the same for every inertial observer yet somehow they have different quantitative values for c.
JesseM said:With quantum field theory I think this is true, but back when the only law of nature involving c was Maxwell's laws, couldn't one have argued that Maxwell's laws are not really fundamental, but just a description of the behavior of a certain physical medium filling space (the aether)?
After all, no one says that since observers at rest relative to the atmosphere measure sound waves in air to have the same speed in all directions, then this must imply by the first postulate that sound waves in air must have the same speed in all directions in every frame (even in a universe where all of space was filled by such an atmosphere).
The important part of the 2nd postulate is that the speed of light does not depend on the speed of the emitter. This might seem "obvious" nowadays, but it was not always so. You could formulate a theory, consistent with the first postulate, in which two light sources moving at different speeds would emit light at different speeds (both speeds relative to a single observer). The 2nd postulate can be paraphrased by saying that it's impossible for any photon to overtake another photon traveling in the same direction. This does not automatically follow from the 1st postulate alone.rbj said:i think the 2nd postulate was there for clarity and was not strictly needed.
DrGreg said:The important part of the 2nd postulate is that the speed of light does not depend on the speed of the emitter.
This might seem "obvious" nowadays, but it was not always so. You could formulate a theory, consistent with the first postulate, in which two light sources moving at different speeds would emit light at different speeds (both speeds relative to a single observer). The 2nd postulate can be paraphrased by saying that it's impossible for any photon to overtake another photon traveling in the same direction.
JesseM said:With quantum field theory I think this is true
JesseM said:but back when the only law of nature involving c was Maxwell's laws, couldn't one have argued that Maxwell's laws are not really fundamental, but just a description of the behavior of a certain physical medium filling space (the aether)? After all, no one says that since observers at rest relative to the atmosphere measure sound waves in air to have the same speed in all directions, then this must imply by the first postulate that sound waves in air must have the same speed in all directions in every frame (even in a universe where all of space was filled by such an atmosphere).
DrGreg said:The important part of the 2nd postulate is that the speed of light does not depend on the speed of the emitter. This might seem "obvious" nowadays, but it was not always so. You could formulate a theory, consistent with the first postulate, in which two light sources moving at different speeds would emit light at different speeds (both speeds relative to a single observer). The 2nd postulate can be paraphrased by saying that it's impossible for any photon to overtake another photon traveling in the same direction. This does not automatically follow from the 1st postulate alone.
Once you've accepted light's independence from the motion of its emitter, the fact that all observers calculate the same numeric speed is a consequence of the 1st postulate. (And you also need to explicitly state that the speed of light is not infinite, otherwise Newtonian theory would satisfy both postulates.)
You are right that the second postulate follows from Maxwell's equations. The point is that you don't need the whole of Maxwell's theory to logically develop the theory of relativity; the second postulate (together with the first) is sufficient.mdeng said:I am still not clear. Didn't Maxwell's equation say (implicitly, and made explicit by Einstein) that light speed c is regardless whether the observer is flying toward the light or, stated it in another way, the emitter is flying toward us? Therefore, neither overtaking or undertaking ever would happen.
Indeed that was the case when he first formulated them; I believe everything in his equations was measured relative to a postulated aether. However, experiments performed in the years leading up to the formulation of Relativity indicated that Maxwell's equations appeared to be true in moving frames too, which led Lorentz to formulate the Lorentz transformation and later led to Einstein's Special Theory.mdeng said:Perhaps Maxwell assumed there was aether and perhaps that was his basis of the equation.
This way of measuring motion is called by various authors "proper speed" or "celerity". The celerity of light is infinite. And, for massive objects, momentum = invariant mass * celerity. And celerity = c * sinh(rapidity).jtbell said:In calculating this "speed", you're taking the distance traveled as measured in one reference frame, and dividing it by the time as measured in another reference frame. This number is definitely of practical significance to space-travelers, but I think most physicists would resist calling it "speed" because of this mixing of reference frames. Unfortunately, I can't think of a good word to use instead of "speed" here.
DrGreg said:Indeed that was the case when he first formulated them; I believe everything in his equations was measured relative to a postulated aether. However, experiments performed in the years leading up to the formulation of Relativity indicated that Maxwell's equations appeared to be true in moving frames too, which led Lorentz to formulate the Lorentz transformation and later led to Einstein's Special Theory.
DrGreg said:The point is, to understand relativity, you don't need to understand Maxwell's equations (partial differential equations which require a moderately advanced knowledge of calculus). It's sufficient to understand the two postulates (no calculus required, until you get to acceleration and gravity).
In essence I'm agreeing with rbj that "2nd postulate was there for clarity and was not strictly needed" provided you accept Maxwell's equations; but if you include the 2nd postulate then you don't need to bring Maxwell into it at all.
mdeng said:While Maxwell's equation did not mention motion,
rbj said:in fact, i knew i mentioned this recently before:
\oint_C \mathbf{B} \cdot \mathrm{d}\mathbf{l} = \mu_0 \iint_S \mathbf{J} \cdot \mathrm{d}\mathbf{S} = \mu_0 \iint_S \rho \mathbf{v} \cdot \mathrm{d}\mathbf{S}
d\mathbf{B} = \frac{\mu_0}{4\pi} \frac{(\mathbf{J}\, dV) \times \mathbf{\hat r}}{r^2} = \frac{\mu_0}{4\pi} \frac{(\rho \mathbf{v}\, dV) \times \mathbf{\hat r}}{r^2}
\mathbf{F} = q \cdot(\mathbf{E} + \mathbf{v} \times \mathbf{B})
what do you think they mean by \mathbf{v}? what did they measure it against?
\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}
\nabla \cdot \mathbf{B} = 0
\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}
\nabla \times \mathbf{B} = \frac{1}{c^2} \left( \frac{\partial \mathbf{E}} {\partial t} + \frac{\rho}{\epsilon_0} \mathbf{v} \right)
more mentions of motion.
mdeng said:Is this motion of the EM in "aether", or motion of the observer's frame through aether?
rbj said:well, that was the original confusion. when they did experiments it was the motion relative to themselves, the observers. but the theory intended that the velocities were absolute and being that these velocities would be greatly different in greatly different reference frames, then the numbers going into the equations would be different and different results would come out. this was something that they worried about which is why they wanted to get a handle on about how fast (and which direction) we were moving through the aether (so they would know how much to fudge their numbers for velocity). that is, if i am not mistaken, what Michaelson and Morley were trying to determine. in doing the experiment, they got a little surprize.
W.RonG said:Hi everybody. I hope this isn't taken as barging in since I'm brand new here, but I did sign up expressly to offer a solution to mdeng's question. I think rbj provides a key to the answer in mentioning Planck time and Planck distance. These are the smallest units of each respective dimension, so it seems to me that anything (object, force, effect, whatever you want to call it) can only traverse one unit of Lp during one or more units of Tp. The fastest possible speed is therefore based on one unit of Lp per each unit of Tp. To go any faster would require fractional Tp to travel one Lp. The speed of light is simply our calculation based on familiar distance, a large multiple of Lp, divided by familiar time, a large multiple of Tp. Rbj gave equivalent measures of these quantities in an earlier post. To mdeng, does this help to see the "speed limit" of (quantized) space-time?
BTW I hope I will be able to participate in other conversations as well, since I also have some questions and possibly some answers.
Thanks all,
Ron
p.s. is there a place for intros? I didn't see any.
W.RonG said:Hi everybody. I hope this isn't taken as barging in since I'm brand new here, but I did sign up expressly to offer a solution to mdeng's question. I think rbj provides a key to the answer in mentioning Planck time and Planck distance. These are the smallest units of each respective dimension, so it seems to me that anything (object, force, effect, whatever you want to call it) can only traverse one unit of Lp during one or more units of Tp. The fastest possible speed is therefore based on one unit of Lp per each unit of Tp. To go any faster would require fractional Tp to travel one Lp. The speed of light is simply our calculation based on familiar distance, a large multiple of Lp, divided by familiar time, a large multiple of Tp. Rbj gave equivalent measures of these quantities in an earlier post. To mdeng, does this help to see the "speed limit" of (quantized) space-time?
BTW I hope I will be able to participate in other conversations as well, since I also have some questions and possibly some answers.
Thanks all,
Ron
p.s. is there a place for intros? I didn't see any.
Xeinstein said:I think Einstein's relativity is a classical theory, so it has nothing to do with Planck
I agree with what you say about "changes" in dimensional constants like c being meaningless, but it seems to me that W.RonG's post was about the notion that quantized spacetime was somehow essential to explaining the invariant speed of light, whereas we can certainly use Planck units (which are just based on manipulations of some other constants like G and h) without committing to any notion that space and time are quantized as opposed to infinitely divisible.rbj said:i think that the fact that we don't measure anything except against like-dimensioned quantities means that whether the dimensionful parameter is c or G or \hbar or \epsilon_0, any variation of any of these dimensionful parameters is "operationally meaningless" (those are Michael Duff's words) or "observationally indistinguishable" (those are John Barrow's words). and that does have something to do with Planck Units.
mdeng said:What is the physics answer to the question of why light has an invariant speed
to anyone and everyone, other than this is what light is?
