Halls of Shrewd'm / US Policy❤
No. of Recommendations: 3
I thought this was interesting.....
https://bigthink.com/hard-science/photons-light-ti...At light speed, Einstein's equations break down and nothing makes sense
Everything everywhere all at once.
The relationship of light to time is nonintuitive. Mathematical limits allow us to figure out what happens to photons at the exact speed of light where Einstein's equations break down. At the speed of light, clocks stop ' and the Universe is shrunk to zero size.
... more at link
No. of Recommendations: 2
That's why the "speed limit" is the speed of light. The denominator of some equations goes to zero, and a mathematician would say it becomes "undefined". Time dilation is real (we've measured it). The universe seems to twist everything to make sure the speed of light is the same in every inertial reference frame.
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Paradoxically, the fabric of space itself can and does expand faster than the speed of light, making the outer regions of the universe inaccessible and unknowable.
No. of Recommendations: 1
Yes, but I suspect that is a function of geometry. For example, it is possible to have a lighthouse whose beacon is spinning so quickly that the spot of light in the distance (at some distance "r") is moving faster than c, even though the rotation of the lamp is not faster than c, nor is the actual light beam.
In this case, probably a function of 4-D geometry (which we can't visualize, being only 3-D creatures). But we can describe it mathematically.
No. of Recommendations: 0
Yes, but I suspect that is a function of geometry. For example, it is possible to have a lighthouse whose beacon is spinning so quickly that the spot of light in the distance (at some distance "r") is moving faster than c, even though the rotation of the lamp is not faster than c, nor is the actual light beam. - 1pg
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That makes for an interesting thought experiment. As the lighthouse beams radius approaches the point where the "tip" of the light beam approaches the speed of light, what would it look like if you could observe it? Perhaps better to visualize some distant wall against which the light beam sweeps. Rather than extending r to some humongous distance, you just keep accelerating the rotation of the beacon.
At slower speeds, the beam traces a continuous path across the wall. This is what we experience in everyday life. But as the sweep speed reaches and exceeds c, it seems to me the sweep would not be continuous but rather become a series of spots separated first by the planck length, then as speeds continue to increase past c, the separation of the spots would increase I suppose all the way to infinity.
The size the "spot" seems like it would have to shrink ultimately to the diameter of a single photon, if a photon can even be said to possess such an attribute. Perhaps it is better described as the beam disappearing altogether but then do you still have a beam at all after c is reached?
No. of Recommendations: 4
I think the intensity may go down (probably would), but remember that once a group of photons are emitted from the beacon, they travel at c in a straight line. They aren't aware (to my knowledge) of the photons before nor after. If we assume the photons are emitted continuously, and in large numbers nearly simultaneously, they all follow their trajectory towards your wall. Fewer of them would strike any given area on that wall if the beacon is rotating faster, which is why I think we'd see an apparently dimming. But the spot on that wall would appear to be exceeding c, even if nothing in the system we've described is exceeding c.
No. of Recommendations: 2
According to current theories in cosmology, the universe is expanding, and the rate of expansion is increasing. However, it is important to note that the expansion of space itself does not violate the laws of physics, including the speed of light.
The expansion of the universe is not caused by objects moving through space, but rather by the space between objects increasing. This means that even if two objects were moving away from each other due to the expansion of space, they would not be violating the speed of light, as they are not moving through space itself.
Furthermore, while the expansion of the universe may make some regions of space further away and harder to observe, it does not make them completely inaccessible or unknowable. Cosmologists are able to study the universe through a variety of methods, including observing light from distant objects and studying the cosmic microwave background radiation, which provides information about the early universe.
So while the expansion of the universe may present challenges to our ability to observe and understand it, it does not necessarily make any parts of the universe completely inaccessible or unknowable.
No. of Recommendations: 6
For example, it is possible to have a lighthouse whose beacon is spinning so quickly that the spot of light in the distance (at some distance "r") is moving faster than c, even though the rotation of the lamp is not faster than c, nor is the actual light beam.Each individual photon is travelling at c and, ignoring nearby large masses, is travelling in a straight line. The fact that the next photon emitted by the beacon is pointed in a new direction that seems to be a long way from the prior emission is immaterial. The photons are independent.
Where it gets interesting is if you have a beam of electrons travelling in a circular orbit at very close to the speed of light. Because they are changing direction as they go around the storage ring they are accelerating and they emit photons as a result. In the rest frame of the electron the emission is isotropic but in the rest frame of the lab there is a Lorentz transformation which focuses all the light into a narrow cone in the forward direction so that the light is always at c. This is known as synchrotron radiation and is a valuable tool for studying matter (or an annoying waste product if you are a high energy physicist).
c.f.
https://en.wikipedia.org/wiki/Synchrotron_radiatio...Rgds,
HH/Sean
No. of Recommendations: 6
Most folks are aware of the Doppler effect and the red-shift observed in stars and galaxies that are receding from us due to the expansion of the universe. Another fun aspect of synchrotron sources is that the light they emit is blue-shifted by that same Doppler effect (aka Lorentz transformation).
The idea that accelerating electrons emit light shouldn't be surprising: If I drive an antenna by varying the applied voltage with a frequency between 600 and 1500 kHz it will emit AM "radio waves" (aka light) which will then drive another (receiving) antenna causing electrons in that antenna to oscillate and using a germanium diode one can hear that signal in one's earphones. So you can think of the electrons in the storage ring as you would electrons in an antenna. The only difference is that the storage ring uses microwaves to accelerate the electrons because they are in a vacuum chamber rather than an antenna. So the electrons are accelerated using microwaves. They (in their rest frame) re-emit that microwave radiation as they accelerate (change direction). But because they are at 0.99999c the light that we see in the laboratory is blue-shifted into the x-ray regime. The result is a broad spectrum of light centered near 0.1 nm (1 Angstrom), which is the sweet spot for both x-ray diffraction and spectroscopy.
Rgds,
HH/Sean
No. of Recommendations: 1
Good stuff HH. Thanks for posting.
No. of Recommendations: 3
This "lighthouse" experiment has been evidenced many times by using an oscilloscope and adjusting the angle of incidence of the stream of electrons to a sufficiently narrow angle to geometrically increase the trace across the oscilloscope screen "above the speed of light".
As there is nothing but a concept moving across the oscilloscope screen, no laws of physics are violated. Each individual electron, (if we can refer to them as such), violates no cosmic speed limits.
fd
