Speed of Light
8 Jan 2007 16:39:13 UTC
Topic 192280
(moderation:
Listen, I have no illusions that my intellect is even in the same ballpark as most of you who post here. I run e@h just to give my computers something to do.
Queston #1: Am I right that the speed of light is consistent, regardless of the velocity of the person viewing it? Meaning if I were in a car driving the speed of light and I turn on my headlights I would observe the light from my headlights exactly the same as if I were sitting at a stop light?
Question #2: If #1 is accurate wouldn’t time be observed consistently under the same set of circumstances mentioned above?
Speed of Light
)
Yes, except that a car (like any other object with mass) can’t be made to move at quite the speed of light; we have to qualify that with “almost�. But when the relativistic formula for adding velocities is used, if either of the addends is c, so is their sum; accordingly the car’s speed turns out to be irrelevant.
I’m not sure what you’re asking here. As long as you’re careful to specify—and stay within—a single inertial frame of reference for measuring time and distance, SR (Einstein’s special theory of relativity) will provide a consistent description of the situation. But it’s often counter-intuitive, especially concerning such notions as simultaneity.
Einstein's Theory of
)
Einstein's Theory of Relativity dictates, that any object consistent of matter-energy, will increase in mass expedentially while reaching the speed of light. Dictating, that mass would be infinite at the speed of light, assuming the energy required to push infinite mass to infinite speed would be infitine energy. So, impossible. Unless you get into folding space, and sub-space theory, which even in those cases, you may end up at the same distance as 50 AU from your starting position, but, in relative terms, your vessel would only have been traveling at a sub-light speed, but in a fold in space, where dynamics are different, and don't retain the same linear distance. Which sounds much alike Star Trek. But not far off, considering, Star trek is wrapped around the hypothesis and theory's of well respected scientists. But all in all, IT'S NOT PROVEN!! lol.. Gotta keep telling myself that. Otherwise, I could go crazy, build myself a trashcan, and try to jump to warp speed from a low flying glider. BEAM ME UP SCOTTY!
d3xt3r.net
RE: Queston #1: Am I right
)
Young Einstein asked himself much the same stuff - what would he see if he caught up with a light wave. Given that light can be modelled as oscillating electric/magnetic fields then would they stop wiggling, ie. freeze, if one travelled at light speed? History records the tremendous success of predictions based upon assuming a constant light speed. BUT he added in the 'relativity' requirement that the laws describing ALL physical phenomena should have the same form in all reference frames and wound up with deducing a change in the nature of time ( AS MEASURED BY CLOCKS ).
The short answer is that constancy of light speed, regardless of who measures it, demands that observers moving relative to each other cannot in general agree on the temporal/time order of spatially/physically separated events. Because light speed is finite and independent of anyone's situation then relative lags occur in the reception of light signals by each measuring party ( because it doesn't travel across any gaps instantly ). We don't notice this everyday because :
- we are 'close' to our surrounding events that 'signal' us.
- we can't perceive 'small' time intervals ( unaided ).
- light is really, really 'fast' ( ie. seven times around the world in one second ).
So light is effectively infinitely fast for everyday purposes, and not surprisingly was thought to be so for much of history. Humans have developed in that sensory experience so have no good intuition beyond it.
Nonetheless if two observers can't agree on the difference/order in timing of two events, then that includes clock ticks or other 'regular' behaviour. Hence all timing issues are relative to who is doing the measuring, but if you know the details of the relative movement of two observers then you can convert data recorded by one into what would then recorded by the other ( for the same events ).
Cheers, Mike.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
RE: Einstein's Theory of
)
The ‘bottom line’ remains the same, but I don’t think it’s fashionable any more to talk about the mass of fast-moving objects increasing, especially without making it clear that the contingent “relativistic mass�, as opposed to the intrinsic “invariant mass�, is meant. The modern tendency is to describe relativistic effects in terms of spacetime geometry (e.g. the inclination of one observer’s world-line to another’s) rather than altered properties of the objects concerned. From this point of view notions like relativistic mass and gravity-as-a-force, although useful for paedagogical purposes to build bridges from Newton to Einstein, are ultimately misleading.
RE: RE: Question #2: If
)
With respect to the LIGOs, is the Earth considered a single inertial frame of reference? I googled 'failure of simultaneity at a distance' and just read about the Andromeda Paradox, and so considering the separation in space-time between the LIGOs, coupled with the fact that one LIGO could be accelerating away from a source while the other LIGO is accelerating towards the source, how profoundly does this affect searches for coincident signals, especially at distances of megaparsecs from the source? Maybe better phrased, is there more of a phase shift in the signal than just the milliseconds that it takes light to go from one LIGO to the other?
I thought that if one LIGO detects a signal, say by matching it to a template of a chirp waveform of an inspiral event, then the other LIGO should detect the same signal, within a few milliseconds (before or after) the first LIGO. But the Andromeda Paradox (or "Rietdijk-Putnam-Penrose" argument, or failure of simultaneity at a distance) makes it sound like a coincident signal could have a temporal displacement of years instead of milliseconds, depending on the distance to the source, and on which section of the source's worldtube that each LIGO is observing at the present instant. Is that true?
But if you've detected a signal with one LIGO, how can you know what should be detected at the other LIGO if you don't know the direction/distance to the source (i.e., the section of the source's worldtube that the other LIGO is observing)? And how can you determine the direction/distance to the source in the first place, with just one LIGO? (In the example given for the Andromeda Paradox, one observer is stationary while the other observer drives past in a car, simply accelerating towards the source, and so no relativistic velocities are involved to cause the phase difference between observers in this example.)
It's probably easier to state
)
It's probably easier to state that the inertia of massive bodies increases with speed. This implies that it requires more force/energy/momentum input to induce a given velocity increase, as you go faster. You could then 'blame' the mass changing for that greater 'sluggishness'. I guess this helps to tie it in with our low speed intuition and thus make Newtonian laws the low speed approximation to Relativity.
With regard to phase shifts other than due to the inter-LIGO separation: well I guess we are going to find out!! The Andromeda 'paradox' seems pretty boring really - we have a similiar problem here in Chum Creek, as by running to meet the mail contractor I can get correspondence earlier than if I sat in the lounge and waited. Does that cause a crisis in understanding the power bill that came? There's no uncertainty as to the outcome of the decision to charge me the money, just that of when I knew of it. Now you might accumulate a 'phase' change while driving along, but are those slanted axes ( in the Wiki diagram Figure 5 ) going to remain so for the entire time it takes light to come from Andromeda? You see what's implied? Andromeda is ~ 2 million light years away, and by going along at car type speeds I could accumulate a day or two of time difference with respect to another observer. So this 'paradox' is a signal that suggests we need to go off the inertial frames assumed in that description and go to GR. From memory that analysis uses retarded time ( t - x/c ) to describe the waveform, accounting for any movement towards mail contractors. :-)
To triangulate a source in the sky you pretty well need three distinct IFO locations to be sure ( and note here that LISA has a triangular design ). Since they're are all attached to the Earth there's unlikely to be any mutual velocites or accelerations large enough to attain relativistic significance in the sense you seem to be suggesting. Whatever you think of the Earth as a frame compared to the cosmos, all the LIGO are on it!
Cheers, Mike.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
Thanks Mike, I can't help
)
Thanks Mike,
I can't help wondering if such a temporal displacement could be used to observe distant Gamma Ray Bursts in their entirety, by utilizing two detectors orbiting in the same plane, but in opposite directions (probably concentric rings of several detectors per ring would be required). For a source that's both sufficiently far away, and close enough to the plane of the detectors, the signal would be detected in one ring before it would be detected in the other. When the signal is finally detected in the second ring, could the delay be used to provide a measure of distance independent of optical sources in the same vicinity (or other means used to determine distance)?
Would it be possible to test this 'paradoxical' aspect of relativity by using just two detectors (orbiting the Earth in opposite directions, but in the same plane) and an object like a pulsar (sufficiently far enough away)? There should be a phase shift in the period of the pulsar proportional to the rate at which the detectors accelerate towards (and away from) the source, right? Has an experiment like this been performed already?
RE: I can't help wondering
)
Don't we already have that? The orbiting gamma observatories?
I guess you could call that parallax, triangulation or somesuch. Each detector will be the centre of some light/photon sphere(s), the intersection(s) of which hopefully will specify a reasonably localised/unique volume out there somewhere - given that you know the relative positions and timings of your devices.
This means that one deduces the cosmic position by ( hypothetically ) sending the signals back out from each detector with the known phase delays, and see what points/volume they commonly converge upon - if this is unique then you infer this as the source location.
A GPS receiver pretty well does this ( with the more satellites the better ), as it finds itself on the overlapping portions of wave fronts radiated by the GPS satellites. The GPS signal not only times pulses but encodes the detail of who/what/where sent them, and all is corrected by known relativistic effects ( big topic ). LIGO uses GPS which in turn relies upon the best Caesium clocks.
I think the Andromeda Paradox is quite a red herring actually, and I feel is readily resolved if you examine the prolog to it:
... which is another way of implying that we really need to know the habits of Andromedians - like do they have speeches before they send out space armadas ( or vice versa )? - before we can claim paradox. The example is cleverly anthropised to suggest a sequence of causation but many physical events are indifferent to time sequence. What I mean is that we really have an implicit/hidden third observer/process who can inform us of the local Andromedian sequence of events. After all the history must be consistent in it's 'own' frame. Then we can compare what we see down the light-line later. If you don't have an observer in Andromeda why are we assuming anything about sequence? If you didn't measure and communicate that to the near Earth frames how can we claim a problem?
The real kicker is that the descriptive mode actually subtly changes, without announcement, from discussing two nearby local observers to the God's eye view ( 'I know what happens in Andromeda' ). Choose one or the other. Einstein only outlined comparisons between frames, so the paradox results from describing 'above' the frame level of description - by excluding Andromedian local knowledge/history not being communicated to Earth.
So what you actually have is a three pairs of frames to 'resolve' events between now. In any case the last bit is wrong:
What will be computed as the same ( in inertial frames, in 'flat' space ) is
x^2 + y^2 + z^2 - (c^2 * t^2)
[ x, y, z and t the co-ordinate differences BETWEEN some two events as measured in SINGLE given frame ]
with the last term, bracketed, accounting for light flight time. If you give me those two Andromedian events then ( sets of ) frames can be chosen so that speeches and invasion fleets are simultaneous ( one choice only ); speeches come before invasion fleets ( infinitely many choices); or invasion fleets come before speeches ( ditto ).
I'm generally stating that, to be useful, what you mean by 'X' is what you measure of 'X' in a given frame and all else might be assumption/models so beware of inconsistencies.
I think the binary pulsar systems would fit the bill here, going to a full GR examination too. The radio telescopes are twirling around on Earth and the pulsars are dancing with each other. Accelerations at either end. That binary system discussed here a few months ago, which thread? You may recall ( I think ) the terrestrial findings referred into the solar system barycentre frame; followed by slicing off the proper motion of the pulsar system with respect to that; to finally isolate the 'native' GR components of interest.
Cheers, Mike.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
RE: Don't we already have
)
Well, there are instruments up there looking (SWIFT, INTEGRAL, HETE, and a couple others?), and there's a network in place such that when any one detector observes an event, a notification with approximate coordinates is immediately sent out to all interested parties, whose instruments & telescopes can then subsequently be trained on the event. However, this group of detectors isn't physically arranged to take advantage of the fact that the observed event will occur at different times for detectors with differing relative motions, since simultaneity fails at a distance, and all the more so as the distance from the event increases.
So for a GRB that's far enough away (and I think most thankfully are), it should be possible to detect the event in the “future looking� detector, which then computes the coordinates and relays them to the detector that's more stationary (relative to the detector that's more 'future looking', and to the event itself). This second detector is orbiting in the opposite direction from the first, and hence is displaced from the 'future looking' orientation of the event's worldtube by some amount that's proportional to difference in velocities of the detectors and the distance to the event. The net effect is that the first detector can provide advanced warning to the second, of an event (the GRB) that would have otherwise occurred at both detectors at the same time, except for the fact that relativity says this simultaneity fails from one inertial frame to the next. If the GRB is far enough away, meaning a great enough displacement in the timing of the observations of it from the differing inertial frames of the detectors, then it should be possible to have the second detector trained on the event, ready to observe it, before the event even occurs in that inertial frame. Shouldn't it?
I don't think I understand it well enough to try doing the maths; maybe the Earth doesn't have enough mass to anchor the orbiting detectors such that the difference in their relative velocities could generate adequate 'failure of simultaneity', but it seems the distance to most GRBs would be more than enough...
Also, to maximize the effect, you'd want the orbiting detectors and the event to ideally be all in the same plane... but with a single set of concentric rings of orbiting detectors, and GRBs occurring at about one per day, you might have one per year where the GRB occurs within a degree of the plane that the detectors are orbiting in....
RE: Well, there are
)
Yeah, but the Andromedian example pre-supposes a particular setup for the frames - in particular the history of movement prior to the instant when the axes coincided. The argument remains valid ( such as it is ) only if the frames have stayed inertial - in this case since the light left Andromeda. The 'paradox' is a comment on the differing information received by the two observers due to their persistent mutual disagreement about time passage ( the slanted axes ).
Well, yes, but we are not going to get days of advance warning here - certainly no less than the light flight time between the two detectors, by which time the GRB pulse may well have beaten us to the second device. :-)
Orbiting etc implies accelerations/gravity and whatnot so then we'd have to move to GR to describe.
Cheers, Mike.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal