The discussion centers on the invariance of the speed of light as perceived by moving observers, emphasizing the implications of Special Relativity. Participants clarify that while the length of a light beam remains constant in its rest frame, measurements of its length and duration differ across frames due to Lorentz transformations. The relativistic Doppler effect is highlighted as a crucial factor in understanding these discrepancies. Ultimately, the conversation underscores the necessity of adopting a four-dimensional spacetime perspective to reconcile classical notions of speed with relativistic physics.
PREREQUISITESPhysics students, educators, and anyone interested in the principles of Special Relativity and the behavior of light in different reference frames.
Speady said:The light beam remains the same length.
No it doesn't. Consider a light beam of length ##L## in some frame ##S##. The front has coordinates ##x=ct## and the back has ##x=ct-L##. In another frame ##S'## we get (from plugging ##x=ct-L## into the Lorentz transforms) that ##x'=\gamma(c-v)t-\gamma L## and ##t'=\gamma(1-\frac vc)t+\frac{v}{c^2}L##. We can eliminate ##t## to get ##x'=ct'-\gamma(1+\frac vc)L##. It's then trivial to observe that the primed frame sees the front of the beam at ##x'=ct'## and hence that the length of the beam in this frame is ##\gamma(1+\frac vc)L##, not ##L##.Speady said:The light beam remains the same length.
The distance you call the length depends on what measurement you choose to call length. The two frames are not actually measuring the same thing when they both measure what they call the length of the beam.Speady said:So what? A ray of light is not affected by an observer, right?
Note that ##\gamma(1+\frac vc)## is the relativistic Doppler factor in disguise, as of course it must be.Ibix said:the length of the beam in this frame is ##\gamma(1+\frac vc)L##, not ##L##.
Other frames do not agree that the value you call ##a## is the duration of emission, due to time dilation. Nor do they think that the emitter was stationary, which you implicitly assume. Thus they calculate a different length using (a slight generalisation of) your formula.Speady said:We determine the length of the light beam by transmitting it for a seconds. The length is then a x c km. The length then no longer needs to be measured, but can be used as an unchanging datum.
Your definition of its length changes, however, so the value of what you call length changes.Speady said:A light beam does not become shorter or longer when I start moving.
You are aware (I know you are because I've told you on earlier threads) that the speed of light from moving sources has been measured and it is always the same. So your conclusion is inconsistent with reality.Speady said:Dividing length and duration always gives a different relative speed between me and the light beam.
I think this is not correct. A fixed setup has always been used for measurement.Ibix said:the speed of light from moving sources has been measured
You are retreading arguments you've been told are wrong before.Speady said:I think this is not correct. A fixed setup has always been used for measurement.
We can call it four-velocity!Speady said:If you replace classical time and space with something else, then you can no longer speak of speed. Speed is defined as length divided by duration. If "length" and "duration" no longer apply, then also invent something else for "speed", but do not call it speed anymore.
The important quantity is not the length of the light beam, but the length of the optical path.Speady said:We determine the length of the light beam by transmitting it for a seconds. The length is then a x c km. The length then no longer needs to be measured, but can be used as an unchanging datum.
The speed of light from moving sources has indeed been measured. For a collection of more than a dozen such experiments, see section 3.3 here:Speady said:I think this is not correct. A fixed setup has always been used for measurement.Ibix said:the speed of light from moving sources has been measured
Every position reported by every GPS receiver ever….Speady said:I think this is not correct. A fixed setup has always been used for measurement.
If you know the length of the bus you can divide by the time it takes to pass you to get its speed. That bit is fine - a bit back-to-front, but it works. @Speady's problem is that he doesn't acknowledge that he needs to recalculate the length of the light beam when he changes frame. That means he's using a Newtonian model and (unsurprisingly) having trouble reconciling it with an invariant speed of light.Dale said:The important quantity is not the length of the light beam, but the length of the optical path.
When you calculate the speed of a bus you do not take the length of the bus and divide by the travel time. You take the length of the bus’s path and divide by the travel time.
Yeah, but other than that....Nugatory said:Every position reported by every GPS receiver ever….
Every astronomical observation of light emitted or reflected by anything not on earth….
Every use of radar to track moving objects…
What have the Romans ever done for us?Vanadium 50 said:Yeah, but other than that....
You're not being rude at all. You are, however posting imprecise statements, which you have probably picked up from popular science sources.L Drago said:That is the main function of general relativity by Einstein which describes universe as 4D where 3D space and 1D time. Space time fabric. The more the mass, the more the curvature in space time and the more the gravity and slower the time. That's also the reason time nearly stops near singularlity of black hole.
Please note that I don't mean to be rude. I am giving my opinion politely.
L Drago, please confine discussion of what you need to learn about black holes to the other thread in which that is already taking place. I understand that you are a seventh grader, so it's perfectly fine that you still have a lot to learn about black holes. But since that is the case, you should not be making statements about them, particularly not in other people's threads which are not even on the topic of black holes. Please take the time to learn more first. In that other thread you are getting plenty of good information to help you do that.L Drago said:I told nearly stopped not entirely stopped. Because of the immense space time curvature.
Time doesn't nearly stop. Moreover, the curvature depends on the mass of the black hole. Extremely massive black holes have less curvature at the event horizon.L Drago said:I told nearly stopped not entirely stopped. Because of the immense space time curvature.