A constant speed of light in all reference frames? Surely you can't be serious.
in [Relativity]
|
From: Ste on 13 Feb 2010 14:11 On 13 Feb, 18:29, mpalenik <markpale...(a)gmail.com> wrote: > On Feb 13, 12:28 pm, Ste <ste_ro...(a)hotmail.com> wrote: > > > On 13 Feb, 15:04, Sam Wormley <sworml...(a)gmail.com> wrote: > > > > On 2/13/10 7:29 AM, Ste wrote: > > > > > I've been absolutely racking my brain (to the point of getting a > > > > headache) for the last few days about this issue... > > > > Physics FAQ:http://math.ucr.edu/home/baez/physics/index.html > > > http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html > > > It's a shame that the only diagram - which enforces the rigor of > > giving a physical explanation - was in relation to classical mechanics. > > We already established in the other thread that using a different > coordinate system can change a length of an object in the first frame > without changing the length of the object in its own frame. You can > see that from the pictures I uploaded. Although I understood your previous explanation, you didn't really "establish" these facts. You just stated them. But it didn't explain why or how. > If you look at those pictures, you'll see that the rod in the x', t' > frame appears to be longer in the x, t frame. You'll also see that > anything that you put in the x,t frame will appear longer in the x',t' > frame (if we were to use Minkowski spacetime, the lengths would have > contracted, rather than expanded). > > It turns out that if lengths contract and time dilates as predicted by > relativity, the measured speed of light will be constant. That's how > those formulas were derived. Einstein said "what would it take for > the speed of light to appear constant in all frames," and it turns out > the answer is that lengths have to be measured differently and clocks > have to run differently. Indeed, but that doesn't explain *how* the clocks come to run slower, or *how* lengths become shorter. And indeed, it doesn't explain how those observations can be true from *both* perspectives. We're invited to just accept it as a fundamental truth, without any underlying explanation. > You keep asking why--what's the physical *reason* that lengths are > measured differently and clocks run differently, and once again, it's > all down to a choice of coordinate system. Why does a moving > observing use a different coordinate system than one who isn't > moving? Because that's the *definition* of moving. Moving simply > *means* that you've rotated your x and t axis. That even explains why > the distance between two objects changes when they are moving with > respect to one another. If they both have different x and t axes, > then they will get farther apart as they each move along their t axis. I'm afraid I do not accept that my "choice of mathematical coordinate system" is the explanation for this.
From: Ste on 13 Feb 2010 14:40 On 13 Feb, 18:44, PD <thedraperfam...(a)gmail.com> wrote: > On Feb 13, 7:29 am, Ste <ste_ro...(a)hotmail.com> wrote: > > > > > > > I've been absolutely racking my brain (to the point of getting a > > headache) for the last few days about this issue, and it's clear that > > the speed of light (where light is either considered in the form of a > > ballistic photon, or a wave-cycle) cannot, physically, be constant in > > all relative frames, and at the same time be constant when travelling > > between two objects in two different frames. It's a physical and > > logical impossibility. > > > It's also clear that velocities cannot be additive (in the form of > > speed of bullet+speed of gun), and nor can they be subtractive > > relative to a background medium (in the form of speed of propagation > > in medium-speed of source). > > > Take an illustration: > > > A C > > B > > > Where A and B are atoms that pass infinitely close to each other. In > > the illustration, A and B are separated from C by a distance L. A and > > C are stationary relative to each other. B is moving, and approaching > > C at a speed S. A pulse is emitted from both A and B simultaneously > > towards C, at the point when A and B are equidistant from C. > > > Now, clearly, if velocities were additive, then light from B would > > reach C much quicker than light from A. We don't see that, so we can > > dismiss that immediately. > > > Next, if velocities were subtractive, like sound, well that seems like > > a compelling explanation for what we see, which is that light from > > both A and B travel towards C at the same speed. But the presence of > > an absolute medium seems to fall down when one considers that, to be > > consistent with observation, the speed of propagation orthogonal to > > the direction of travel must be the same as the speed in the direction > > of travel. > > > A speed (i.e. a mesure of distance traversed within a period of time) > > cannot possibly be measured constant in all directions within a frame, > > *and* constant between frames, where the frames themselves are moving > > at a speed relative to each other. So how the hell does one reconcile > > this physically? > > First of all, it's a mistake to say that velocities must be either > additive or subtractive, as though those are the only two > possibilities. I think you're taking it too literally - by "additive" and "subtractive, I mean the alternatives are that a object's velocity must cause either an increase or a decrease in the speed of light in a particular direction relative to something. > The reality is that velocities combine this way: v' = (v+u)/(1+uv/c^2) > or this way: v' = (v-u)/(1-uv/c^2). > Now then, the right question might be, why on earth would it be this > way rather than simple addition or subtraction. > > Secondly, if you're looking for a diagram that makes sense of this, > you need to be Googling first for something like "worldline in > Euclidean space". > This will show you what the *meaning* of velocity is on the worldline > diagram. > This will also show you *diagrammatically* what it means to transform > the velocity to a different frame and WHY the additive rule would be > expected if the universe had that geometry (disconnected time and > space dimensions). > Then you can find out *diagrammatically* what it means to transform > the velocity if the universe has connected time and space dimensions, > and just a little playing around with the diagram will reveal the > reason for the odd-looking sum rule above. > > Robert Geroch's book that I've mentioned to you previously has some > good presentations of these diagrams. Tell you what Paul, to clarify my thinking, consider this simple setup: S1 D2 D1 S2 We've got sources S1 and S2, paired with detectors D1 and D2. They're all mechanically connected, so that a movement in one of them produces a movement in all the others - in other words, their relative distances are always maintained. Each source is transmitting a regular pulse of light to its counterpart detector (so S1 is transmitting to D1, etc.), and both sources are transmitting simultaneously with each other. Now, we calculate that a pulse has just been emitted from both sources, and we suddenly accelerate the whole setup "upwards" (i.e. relative to how it's oriented on the page now) to near the speed of light, and we complete this acceleration before the signals reach either detector. Now, do both detectors *still* receive their signals simultaneously, or does one receive its signal before the other? And are the signals identical, or do they suffer from Doppler shifting, etc?
From: Ste on 13 Feb 2010 14:43 On 13 Feb, 19:11, PD <thedraperfam...(a)gmail.com> wrote: > On Feb 13, 1:01 pm, Ste <ste_ro...(a)hotmail.com> wrote: > > > > > > > On 13 Feb, 18:45, PD <thedraperfam...(a)gmail.com> wrote: > > > > On Feb 13, 11:51 am, Ste <ste_ro...(a)hotmail.com> wrote: > > > > > Not really. I'm still struggling to understand what is happening > > > > physically to explain these phenomena (which is not helped by the > > > > dearth of interest in physics in physical, rather than mathematical, > > > > explanations). > > > > Oh, come now. You appear to have bailed on the discussion of > > > relativity of simultaneity, which I was doing with purely physical > > > explanations and a complete lack of math. > > > I think you're being just a bit disingenuous here. > > > I didn't bail on it. I said I felt that your train analogy had a lot > > of extraneous concepts, such as clouds and tracks, > > On the contrary, I *agreed* with you that the clouds (which I never > brought up -- you did) are extraneous, as are the tracks, which is > precisely why the velocities of the train with respect to the tracks > are irrelevant. Indeed, and that is where the analogy ended as I recall. > > and then you didn't > > really go on to say anything more about that analogy or about > > simultaneity. > > I'm sorry, read again. I laid out the plan for where we were going > next. Did you not see that? I did read it again before replying to you, to make sure I hadn't missed anything. I couldn't see your response to me that dealt with the analogy any further.
From: eric gisse on 13 Feb 2010 14:48 Ste wrote: > I've been absolutely racking my brain (to the point of getting a > headache) for the last few days about this issue, and it's clear that > the speed of light (where light is either considered in the form of a > ballistic photon, or a wave-cycle) cannot, physically, be constant in > all relative frames, and at the same time be constant when travelling > between two objects in two different frames. It's a physical and > logical impossibility. Experiment says otherwise. Alter your preconceptions. [...]
From: PD on 13 Feb 2010 15:07
On Feb 13, 1:11 pm, Ste <ste_ro...(a)hotmail.com> wrote: > On 13 Feb, 18:29, mpalenik <markpale...(a)gmail.com> wrote: > > > > > On Feb 13, 12:28 pm, Ste <ste_ro...(a)hotmail.com> wrote: > > > > On 13 Feb, 15:04, Sam Wormley <sworml...(a)gmail.com> wrote: > > > > > On 2/13/10 7:29 AM, Ste wrote: > > > > > > I've been absolutely racking my brain (to the point of getting a > > > > > headache) for the last few days about this issue... > > > > > Physics FAQ:http://math.ucr.edu/home/baez/physics/index.html > > > > http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html > > > > It's a shame that the only diagram - which enforces the rigor of > > > giving a physical explanation - was in relation to classical mechanics. > > > We already established in the other thread that using a different > > coordinate system can change a length of an object in the first frame > > without changing the length of the object in its own frame. You can > > see that from the pictures I uploaded. > > Although I understood your previous explanation, you didn't really > "establish" these facts. You just stated them. But it didn't explain > why or how. > > > If you look at those pictures, you'll see that the rod in the x', t' > > frame appears to be longer in the x, t frame. You'll also see that > > anything that you put in the x,t frame will appear longer in the x',t' > > frame (if we were to use Minkowski spacetime, the lengths would have > > contracted, rather than expanded). > > > It turns out that if lengths contract and time dilates as predicted by > > relativity, the measured speed of light will be constant. That's how > > those formulas were derived. Einstein said "what would it take for > > the speed of light to appear constant in all frames," and it turns out > > the answer is that lengths have to be measured differently and clocks > > have to run differently. > > Indeed, but that doesn't explain *how* the clocks come to run slower, > or *how* lengths become shorter. But in fact, I gave you a sketch about how one could understand, for example, *how* lengths are frame-dependent, because the definition of length relies on simultaneity, and we were on the way to show that simultaneity is frame-dependent. > And indeed, it doesn't explain how > those observations can be true from *both* perspectives. We're invited > to just accept it as a fundamental truth, without any underlying > explanation. > > > You keep asking why--what's the physical *reason* that lengths are > > measured differently and clocks run differently, and once again, it's > > all down to a choice of coordinate system. Why does a moving > > observing use a different coordinate system than one who isn't > > moving? Because that's the *definition* of moving. Moving simply > > *means* that you've rotated your x and t axis. That even explains why > > the distance between two objects changes when they are moving with > > respect to one another. If they both have different x and t axes, > > then they will get farther apart as they each move along their t axis. > > I'm afraid I do not accept that my "choice of mathematical coordinate > system" is the explanation for this. |