mistermack Posted February 22, 2017 Posted February 22, 2017 I don't think it falls out of that, that any observer will get the same result, regardless of their motion. It says that the speed of light will always be the same, that's all. You could give the speed of sound the same treatment. But different observers will get different figures.
geordief Posted February 22, 2017 Author Posted February 22, 2017 I don't think it falls out of that, that any observer will get the same result, regardless of their motion. It says that the speed of light will always be the same, that's all. You could give the speed of sound the same treatment. But different observers will get different figures. Perhaps you are right . That would explain why Strange described the outcome as conforming to "Galilean Relativity" But I don't think "invariance" is required by Galilean Relativity although Swansont in post#8 does say "That they*ie Maxwell's Equations work (there is a wave equation you can formulate from them) is evidence that c is invariant." Perhaps (I am guessing/surmising here ) the invariance does not "drop out" of the equations but it becomes apparent quite soon after as a consequence . *ie Maxwell's Equations
Tim88 Posted February 22, 2017 Posted February 22, 2017 (edited) Is it possible to highlight the salient feature in Maxwell's mathematics that mean that the invariance of c "jumps out of them" ? Does this invariance "jump out" only in the final equations or can it be seen to be introduced as the maths proceeds earlier on in the working? Does Maxwell base his maths on experimental observation and is there an aspect to these observations that would lead one to say that this particular observation implied necessarily that the speed of propagation of the wave would be the same no matter whether the observer was in relative motion wrt the experimental setup? No, it's not a feature in Maxwell's equations. The fact of the matter is that he had not done what I mentioned in post #21. Instead, he expected a positive result of MMX type measurements (he originally proposed such a measurement). PS: the very neat video to which Strange linked, shows how the speed of light as a *wave speed constant* "jumps out" of the Maxwell equations. Thus a disambiguation may be at its place here... You emphasized that you are not asking here about the constancy of the speed of light (as in the second postulate), but about the invariance (as in the first postulate). Edited February 22, 2017 by Tim88
mistermack Posted February 22, 2017 Posted February 22, 2017 The big assumption is that the permitivity and permeability of free space are always the same, everywhere. Which seems to be true. The same doesn't apply to sound waves in air or water, as the equivalent properties vary with temperature etc. Is the permeability and permittivity of free space dependent on the velocity of whoever measures it? That would seem likely, EXCEPT that the velocity of the observer also affects his clock. So, because of time dilation, an observer will always measure the same values for permittivity and permeability..And hence will always get the same figure for the speed of light.
geordief Posted February 22, 2017 Author Posted February 22, 2017 (edited) p.43 is not visible for me in your link. Anyway, it has been shown that if you assume the validity of Maxwell's equations for a single reference system as well as the validity of the conservation laws (energy, momentum), the relativity principle follows - which implies invariance and limit speed. On revision,I see that you have answered my question as to the (indirect) relation between Maxweĺl's equations and the invariance of c. A bit above my pay grade but I see the path ahead of me. Apologies for not realizing this at the time Edited February 22, 2017 by geordief
Strange Posted February 22, 2017 Posted February 22, 2017 I don't think it falls out of that, that any observer will get the same result, regardless of their motion. Show me where the speed of the observer appears in those equations. It says that the speed of light will always be the same, that's all. Duh. That is kind of the point. You could give the speed of sound the same treatment. Go on then. Show me how the measured speed of sound is independent of the observer's speed through the medium.
mistermack Posted February 22, 2017 Posted February 22, 2017 Strange, you completely missed my point. The speed of sound is NOT independent of the observer's speed through the medium. I didn't say it was. It's always the same, relative to the medium. (in standard conditions) BUT, if the observer's clock operated using sound, ( for example by pinging a sound to a target and measuring the time for the return ping ) then the observer's clock would slow with velocity, and they would consequently always get the same value for the speed of sound, regardless of velocity.
Janus Posted February 22, 2017 Posted February 22, 2017 Strange, you completely missed my point. The speed of sound is NOT independent of the observer's speed through the medium. I didn't say it was. It's always the same, relative to the medium. (in standard conditions) BUT, if the observer's clock operated using sound, ( for example by pinging a sound to a target and measuring the time for the return ping ) then the observer's clock would slow with velocity, and they would consequently always get the same value for the speed of sound, regardless of velocity. If you tried such an experiment with a "sound clock", you would get different answers for the return time of the sound for the same trip distance depending on which direction you sent your sound. A clock aligned with the motion with respect to the medium would tick at a different rate than one aligned perpendicular to it. The point is that an observer with such a clock set up could determine his motion with respect to the medium by pointing his device in different directions and noting the difference in return times. With a light clock he can't. He can perform the experiment, get the same return time in all directions, accelerate to some new velocity, repeat the experiment and get the same results. All his light clocks will always tick at the same rate regardless of the direction they are pointing.
geordief Posted February 22, 2017 Author Posted February 22, 2017 At a bit of a tangent ,would it be right to say that an accelerated observer would measure a different value of c to that measured by an unaccelerated observer? If so, I wonder what might be the minimum/maximum values allowed.
mistermack Posted February 22, 2017 Posted February 22, 2017 If you tried such an experiment with a "sound clock", you would get different answers for the return time of the sound for the same trip distance depending on which direction you sent your sound. A clock aligned with the motion with respect to the medium would tick at a different rate than one aligned perpendicular to it. The point is that an observer with such a clock set up could determine his motion with respect to the medium by pointing his device in different directions and noting the difference in return times. With a light clock he can't. He can perform the experiment, get the same return time in all directions, accelerate to some new velocity, repeat the experiment and get the same results. All his light clocks will always tick at the same rate regardless of the direction they are pointing. That's an interesting point. But, are you assuming that the reflecting target is stationary? I was talking about a clock that co-moved with the observer in it's entirety. So the sender and target are moving through stationary air with the same velocity. In practice, they would be physically attached.
Janus Posted February 22, 2017 Posted February 22, 2017 That's an interesting point. But, are you assuming that the reflecting target is stationary? I was talking about a clock that co-moved with the observer in it's entirety. So the sender and target are moving through stationary air with the same velocity. In practice, they would be physically attached. I am assuming a standard light clock set up, where source and reflector are stationary with each other for both the light clock and "sound clock". At a bit of a tangent ,would it be right to say that an accelerated observer would measure a different value of c to that measured by an unaccelerated observer? If so, I wonder what might be the minimum/maximum values allowed. Everyone measures the local speed of light as being the same.
swansont Posted February 22, 2017 Posted February 22, 2017 Strange, you completely missed my point. The speed of sound is NOT independent of the observer's speed through the medium. I didn't say it was. It's always the same, relative to the medium. (in standard conditions) BUT, if the observer's clock operated using sound, ( for example by pinging a sound to a target and measuring the time for the return ping ) then the observer's clock would slow with velocity, and they would consequently always get the same value for the speed of sound, regardless of velocity. IOW, if you built a crappy clock, it would keep crappy time. That seems completely beside the point.
mistermack Posted February 22, 2017 Posted February 22, 2017 IOW, if you built a crappy clock, it would keep crappy time. That seems completely beside the point. Nobody's talking about a crappy clock. Or are you forgetting that atomic clocks slow as their velocity increases? A sound clock would definitely slow, as it's velocity in the medium increased. And would be stopped altogether, if the clock reached the speed of sound. Doesn't that remind you of anything?
geordief Posted February 22, 2017 Author Posted February 22, 2017 Everyone measures the local speed of light as being the same. thanks
swansont Posted February 22, 2017 Posted February 22, 2017 Nobody's talking about a crappy clock. Or are you forgetting that atomic clocks slow as their velocity increases? A sound clock would definitely slow, as it's velocity in the medium increased. And would be stopped altogether, if the clock reached the speed of sound. Doesn't that remind you of anything? Yes, you are talking about a crappy clock if its performance depended so drastically on its speed. An atomic clock traveling at highway speeds over a 5000 mile trip will lose 1-2 ns, which is barely measurable with a single commercial Cs beam clock (that loss is not really statistically significant, i.e. the noise in the clock will be similar.) How much will your sound clock slow owing to similar motion, and due to this other mechanism?
studiot Posted February 22, 2017 Posted February 22, 2017 Is it possible to highlight the salient feature in Maxwell's mathematics that mean that the invariance of c "jumps out of them" ? Does this invariance "jump out" only in the final equations or can it be seen to be introduced as the maths proceeds earlier on in the working? Does Maxwell base his maths on experimental observation and is there an aspect to these observations that would lead one to say that this particular observation implied necessarily that the speed of propagation of the wave would be the same no matter whether the observer was in relative motion wrt the experimental setup? Geordief you may remember an old saw about two short planks (not referring to you of course) Anyway you might like to consider / be intrigued by this article on the subject of Maxwell's equations, the invariance of c and two short planks.
mistermack Posted February 22, 2017 Posted February 22, 2017 Yes, you are talking about a crappy clock if its performance depended so drastically on its speed. An atomic clock traveling at highway speeds over a 5000 mile trip will lose 1-2 ns, which is barely measurable with a single commercial Cs beam clock (that loss is not really statistically significant, i.e. the noise in the clock will be similar.) How much will your sound clock slow owing to similar motion, and due to this other mechanism? The point is that highway speed is a tiny fraction of the speed of light. If your sound clock was moving at a similar tiny fraction of the speed of sound, then the time dilation would be equally minimal. If your atomic clock was travelling at one tenth the speed of light ( like highway speed is one tenth the speed of sound ), then you would expect some significant affect on the atomic clock.
swansont Posted February 22, 2017 Posted February 22, 2017 The point is that highway speed is a tiny fraction of the speed of light. If your sound clock was moving at a similar tiny fraction of the speed of sound, then the time dilation would be equally minimal. If your atomic clock was travelling at one tenth the speed of light ( like highway speed is one tenth the speed of sound ), then you would expect some significant affect on the atomic clock. So? That's comparing apples to oranges. Clocks move at 50 mph much more often than they do at a reasonable fraction of c. And even a few meters per second is probably a measurable effect for sound.
mistermack Posted February 23, 2017 Posted February 23, 2017 So? That's comparing apples to oranges. Clocks move at 50 mph much more often than they do at a reasonable fraction of c. And even a few meters per second is probably a measurable effect for sound. Quite right. So using a sound clock to measure the speed of sound, is having the same effect as using a light clock to measure the speed of light.
Janus Posted February 23, 2017 Posted February 23, 2017 (edited) Quite right. So using a sound clock to measure the speed of sound, is having the same effect as using a light clock to measure the speed of light.No, for two reasons: The first I've already mentioned, that sound clocks aligned in different directions would "tick" at different rates. and light clocks wouldn't. The second is that with sound clocks an observer traveling with the clock would note that it ticks at different rates depending on its velocity with respect to the medium, while a person traveling with a light clock will never note any change in its tick rate. Edited February 23, 2017 by Janus
Tim88 Posted February 23, 2017 Posted February 23, 2017 On revision,I see that you have answered my question as to the (indirect) relation between Maxweĺl's equations and the invariance of c. A bit above my pay grade but I see the path ahead of me. Apologies for not realizing this at the time That's fine, you are receiving many replies and it's not always clear which are real answers. If you like, I can scan and send you an old paper in which this was done.
mistermack Posted February 23, 2017 Posted February 23, 2017 No, for two reasons: The first I've already mentioned, that sound clocks aligned in different directions would "tick" at different rates. and light clocks wouldn't. The second is that with sound clocks an observer traveling with the clock would note that it ticks at different rates depending on its velocity with respect to the medium, while a person traveling with a light clock will never note any change in its tick rate. You've asserted that they would tick at different rates, but you haven't given any evidence for that. It might be right, but it also might not. As far as the second goes, an observer travelling with the clock could only note that it ticks at different rates, if he had a different clock to compare with it. When it comes to measuring the speed of light, we have no other clocks. Time dilation occurs for everything. Which igoes back to my original point. All observers measure the same value for the speed of light, because they use clocks that slow, with their relation to the speed of light.
Strange Posted February 23, 2017 Posted February 23, 2017 You've asserted that they would tick at different rates, but you haven't given any evidence for that. It might be right, but it also might not. Because they are travelling through the medium at different speeds. When it comes to measuring the speed of light, we have no other clocks. Of course we do. Time dilation occurs for everything. Exactly.
mistermack Posted February 23, 2017 Posted February 23, 2017 Strange, all three of your comments are either wrong, or miss the point entirely. Firstly, clocks aligned at different angles to the motion do NOT travel through the medium at different speeds. Secondly and thirdly, your posts contradict each other.
swansont Posted February 23, 2017 Posted February 23, 2017 Secondly and thirdly, your posts contradict each other. How so? You were talking about light clocks. Nobody actually uses a light clock to measure time. To claim we have no other clocks is ludicrous.
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