Max Born was a long time friend of Albert Einstein and first published his book in 1924 after discussing it with Einstein in a letter.
The passage in question can be found on page 357 in the Dover reprint of 1962 and 1965 which Born edited and approved, showing the relevant mathematics in Einstein notation.
"Therefore the velocity of light is much greater for some directions of the light ray than its ordinary value c, and other bodies can also attain much greater velocities."
Peter Bergmann disagreed but didn't publish his opinion until 1968. The argument was left out of his 1942 book to get the endorsement of Einstein. In the Forward Einstein wrote that much effort went into making the book acceptable. Many researchers agreed with Bergmann and taught their students that way.
In studies of deep space travel the assumption is usually made that c is always constant. Einstein's last word on the subject was that c is constant when gravity does not have to be considered.
Was Max Born Correct That Light Speed Can Sometimes Exceed The Standard Value?
Numerical values of speeds depend entirely on the coordinates (and units) that you choose. The physical constraint is that causality is not violated as long as the speed of information flow does not exceed the speed of light in vacuo.
ZM: It is said that we can see only the areas which are not running away from us with velocities greater than c.
That is often said but not true. The rate of recession due to the Hubble flow exceeds one light year per year for any redshift around or greater than 1.6, we observe galaxies up to a red shift of around 11 and the redshift of the CMB is 1089. In fact the theoretical limit is infinite redshift which would be the horizon of the observable portion of the universe.
Numerical values of speeds depend entirely on the coordinates (and units) that you choose. The physical constraint is that causality is not violated as long as the speed of information flow does not exceed the speed of light in vacuo.
ZM: It is said that we can see only the areas which are not running away from us with velocities greater than c.
That is often said but not true. The rate of recession due to the Hubble flow exceeds one light year per year for any redshift around or greater than 1.6, we observe galaxies up to a red shift of around 11 and the redshift of the CMB is 1089. In fact the theoretical limit is infinite redshift which would be the horizon of the observable portion of the universe.
Dear George,
The fact that the recessional velocity can exceed the velocity of light is not a prove that the local velocity of light is exceeded. In fact since the relationship between the cosmic distance and cosmic velocity involves the Hubbard parameter, which is not known with great accuracy at present. That is to say, it is not really measured but deduced within a theoretical doubful background. For instance, for its determination it is necessary to find the redshift between two any points which only depends of their time separation and it is independent of their real space separation. This needs in fact to assume the velocity of light to make a relationship between them, and therefore the concepts are mixed. In any form this is a prove to state that the velocity of light that we use is smaller than the one associated to this recession velocity!.
On the other hand, going to the general question. The argument that the velocity has projections which can exceed its value is true for a kinetic motion where the motion is only considered, but relativity is more involved with the velocity that light can carry energy and momentum. For instance, the phase velocity of light for one harmonic can be much higher than the velocity of light, but the group velocity cannot. That is the important point to consider when this issue is faced.
Interesting discussion. Some interesting Wikepedia weblinks in this respect:
https://en.wikipedia.org/wiki/Inflation_(cosmology)
https://en.wikipedia.org/wiki/Variable_speed_of_light
https://en.wikipedia.org/wiki/Faster-than-light
https://en.wikipedia.org/wiki/Bell_test_experiments
https://en.wikipedia.org/wiki/Quantum_entanglement
https://en.wikipedia.org/wiki/Action_at_a_distance
Note e.g. quantum entanglement the striking, "classical" phrase by Einstein: "Spooky action at a distance". Regarding this, see also these weblinks:
https://www.technologyreview.com/s/427174/einsteins-spooky-action-at-a-distance-paradox-older-than-thought/
http://www.sciencemag.org/news/2018/04/einstein-s-spooky-action-distance-spotted-objects-almost-big-enough-see
https://www.sciencealert.com/einstein-spooky-action-demonstrated-on-massive-scale-for-first-time
Dear Zbigniew,
My description was only for remember the many different forms to consider the velocity of light. But I didn't want to enter in subtleties in that post for considering explicitally the kind of different media, but obviously they are the ones which makes velocities really very different
https://en.wikipedia.org/wiki/Dispersion_(optics)#Material_dispersion_in_optics
But what is important for me in this discussion is not the medium that I supose always the vacuum but the frequency of the light because it is necessary to use the Doppler effect in the recession velocity that George was mentioning. In such a case what is relevant is that light cannot carry energy and momentum at higher velocity of the light.
Dear Zbigniew,
The energy-momentum is fundamental for the electromagnetic wave and it is conserved independently of the state of motion of the observers. I think that you are forgotting that the photons are always relativistic particles and never classical objects.
Dear Zbigniew,
I have forgotten to add that in 1911 Einstein introduced a variable velocity of light within a gravitational field
c=c0(1+2GM/rc2)
Where M is the mass creating a gravitational field in r where the light is assumed to pass. This is the source of main problem in Cosmology which is still now in a controversy. There are cosmologist who believe that the velocity of light is not constant in the Universe. I don't believe it but this is the arena where I tried to discuss with George for an expanded Universe which follows the Hubble law without entering in different dispersive media.
Maybe not directly within the core of this question thread, still as there have been some comments about photons as relativistic particles here, note on-going experiments slowing down ("freezing") the light down to a halt, i.e. light which isn't moving, see e.g. these weblinks:
https://www.nasa.gov/home/hqnews/2003/may/HQ_news_03176.html
https://io9.gizmodo.com/scientists-freeze-light-for-an-entire-minute-912634479
And do (must) photons have zero rest mass when not moving at all...? Could we measure that zero rest mass “directly”, i.e. measure that it really has zero rest mass? Light rays moving at light speed (!) are bended by large masses (e.g. stars)... i.e. the photons do have mass when moving... e.g. at light speed (c)... gravitional pull between masses. Putting velocity = light speed (v = c) gives infinte mass, time, length and energy in Einstein's special relativity theory equations if the rest mass of light isn’t zero. Why such a special case for light, electromagnetic radiation, gravitons? Is light in reality moving a bit slower (not measured yet) than the "speed of light barrier"... speed of electromagnetic radiation barrier...? That is, could light at rest still have a mass different from zero? And if not, how could it change back and forth between a given mass value and zero mass (between moving and standstill)... what would be the nature behind that? Mass linked to energy through E = mc2 yes and in addition you have the energy and frequency relationship (with Planck's constant) and the speed of light, frequency and wavelength relationship. Or must the existing theory (equations) have to be modified a bit? (not the first time that have happened in the search for the natural laws... and it will not be the last time either...) Gravitional force (gravitons) also propagating at the same speed... i.e. speed of light. All fundamental forces (could they be unified into one?) propagating at speed of light? And then comes Einstein's general relativity theory linking mass to space itself. Waves propagating through space... photons exhibiting both particle and wave properties... i.e. the light particle-wave dualism... clearly heavy and not so light stuff...(!) ;-) The first one to solve this, e.g. unified theory for light explaining all its properties (all observations from different experiments) will for sure get a ticket to Stockholm... to receive the Nobel Prize in Physics...(!) :-)
Yes, in fact for all his different results Einstein would have deserved to receive several Noble Prizes. In 1922 he finally got the Noble Prize for Physics for 1921 for mainly the explanation of the photoelectric effect from his incredible year of 1905, which may be seen as a start of quantum mechanics, i.e. in this case photons with specific and discrete (i.e. quantum) energies as compared to the wave theory for light where the waves are continous, i.e. the particle-wave dualism. So Einstein never got the Noble Prize for all his other great theories and discoveries, including both the special and general relativity theory, where many of his different theories and predictions were "proven to be correct" many years later.
I've never expected speed of an object to exceed local light speed. The mathematics gives imaginary energy, momentum, and mass on every attempt.
The present question is asking if curvature in 4D can change the local speed of light for example when measured under acceleration. This is the meaning of the math Max Born used to introduce the concept. It agrees with one possible interpretation that can be applied to Einstein's technical book on relativity from 1922. The topic begins with equation 107 and the several paragraphs that precede it and follow it. Light speed was shown to vary from standard value in a gravity field, variable L. Einstein used the result in his next unnumbered equation to compute precession of Mercury orbit.
Much is said about limitation of light speed, which seems to be a limitation of vacuum space. Curvature must be in some way a change in optical properties of vacuum space. The book from Max Born has been in publication for a long time including about 30 years while Einstein was alive and active. Einstein did not object to it in any publication I know of.
The answers become important when various groups are considering deep space travel, example the 100 Year Starship initiative.
Thanks to everyone who participated.
Today I and many others received the following weblink from a colleague in Portugal:
https://www.sciencedirect.com/science/article/pii/S0040162517309733
with the article “Is the force awakening?” by Ulrich A. K. Betz (2018) which I recommend you to read.
With respect to space travel, e.g. the following is stated in this article:
“Also the fact that transportation is below average seems to correlate well with the poster-child of technological underachievement: space travel and the inability of humanity to colonize space and the dramatically slower progress vs. what was anticipated fifty years ago.”
And furthermore from the same article (spooky action at a distance):
“Going even further than that, quantum physics has the potential to shatter our entire understanding of reality. This is visible in the so called “Bells Theorem”. In 1935 Einstein, Podolsky, and Rosen published a paper which showed that under certain circumstances quantum mechanics predicted a breakdown of locality “spooky action at a distance”, but doubted this could really happen and thus viewed it as evidence that quantum mechanics was incomplete. Correlations of this sort, however, later were observed experimentally. As Bell proved in 1964, this leaves two options for the nature of reality: The first is that reality is irreducibly random, meaning that there are no hidden variables that “determine the results of individual measurements”. The second option is that reality is ‘non-local’, meaning that “the setting of one measuring device can influence the reading of another instrument, however remote”. In other words, the world is either non-causal or nonlocal, meaning that either causal influences propagate faster than light, or a common-sense notion about what the word “cause” signifies is wrong (Wiseman, 2014; Wiseman, 2015).”
In addition, I’ve posted a separate question thread on ResearchGate for this one about what the next great scientific and technological breakthrough will be, with the title “What will be the Next Force Awakening?”:
https://www.researchgate.net/post/What_will_be_the_Next_Force_Awakening?
Hope to see some interesting thoughts and ideas there.
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