The Prison Built by Einstein

Pentcho Valev

"The Prison Built By Einstein" Scientists are TRAPPED!

Scientists were trapped in 1905 when they started to digest a preposterous nonsense: the speed of light relative to the observer is independent of the speed of the observer. Einstein wrestled with his conscience "over a lengthy period of time, to the point of despair" before positing the nonsense:

"But this seems to be nonsense. How can it happen that the speed of light relative to an observer cannot be increased or decreased if that observer moves towards or away from a light beam? Einstein states that he wrestled with this problem over a lengthy period of time, to the point of despair." https://history.aip.org/exhibits/einstein/essay-einstein-relativity.htm

The speed of light relative to the observer obviously VARIES with the speed of the observer. Assume that a light source emits equidistant pulses and an observer starts moving towards the source:

The speed of the light pulses relative to the stationary observer is

c = df

where d is the distance between subsequent pulses and f is the frequency at the stationary observer. The speed of the pulses relative to the moving observer is

c'= df' > c

where f' > f is the frequency at the moving observer.

write4u

The speed of the light pulses relative to the stationary observer is
c = df
where d is the distance between subsequent pulses and f is the frequency at the stationary observer. The speed of the pulses relative to the moving observer is
c'= df' > c
where f' > f is the frequency at the moving observer.

Allow me to propose a never mentioned scenario based on the premise that
"time stands still @ "c"

Proposition: What if quantum renewal is limited to "c" and cannot complete @ FTL?
i.e. "c" is the absolute maximum rate that reality itself can become manifest and @ FTL one becomes trapped in a quantum suspension between expressed quantum states.

Questions:
a) Does quantum function have any limitations at all?
b) If the doppler effect is stretched to FTL, will there be a wave function at all?
c) Einstein's prison may be a real mathematical/physical fact.

If appropiate , please transfer to "Light particle vs light wave theory

Last edited:

Hartmann352

Light travels at the same speed for all reference frames due to Einstein's theory of relativity. The light would travel away from the fast object at the speed of light to the reference frame of the speeding object, but you would also see the light traveling at the speed of light from a nonmoving reference frame.

Instead, you are having trouble with the invariance of the speed of light, you might prefer an approach that does not use it. It turns out that, if you use only the principle of relativity, you can prove that there are two possibilities. Either there is no finite invariant speed, in which case you get Galilean relativity, or there is a finite invariant speed, in which case you get special relativity. Then it becomes a simple matter of experimentally testing to see which of the two possibilities corresponds to reality.

If you really wanted to derive the invariance of c from time dilation, length contraction, and the relativity of simultaneity, the procedure is straight forward. Time dilation, length contraction, and the relativity of simultaneity together give you the Lorentz transform:

𝑡′=𝛾𝑡−𝛾𝑣𝑥/𝑐2t′=γt−γvx/c2

𝑥′=𝛾𝑥−𝛾𝑣𝑡x′=γx−γvt

Then a light pulse in the unprimed frame is given by

𝑥=𝑐𝑡x=ct

so substituting in we get the equation for a light pulse in the unprimed frame

𝑡′=𝛾𝑡−𝛾𝑣𝑡/𝑐t′=γt−γvt/c

𝑥′=𝛾𝑐𝑡−𝛾𝑣𝑡=𝑐𝑡′x′=γct−γvt=ct′

So the speed of the light pulse is c in the primed frame also. The speed of light is therefore invariant.

Let's examine some history.

Isaac Newton pursued a more philosophical vein. Colours, he insisted, lie not in the medium and not in objects but in light rays—and since colours are qualities, the rays themselves must be made of a material substance. Claiming that his account would undoubtedly stimulate further research, Newton thoughtfully provides full instructions, including dimensions, for an experimental set-up that he had designed to demonstrate—not test—the validity of his propositions. He recommended passing sunlight first through a prism and then through a lens on to a sheet of paper. By moving the paper backwards and forwards through the focal point, the refracted beam can, he reported, be seen splitting into colours and then reuniting into white light. However, even the incomplete trouble-shooting details he provides confirm how tricky it can be to obtain the desired effects.

Isaac Newton in 1686 postulated these three laws:
1. Objects in motion or at rest remain in the same state unless an external force imposes change. This is also known as the concept of inertia.
2. The force acting on an object is equal to the mass of the object multiplied by its acceleration. In other words, you can calculate how much force it takes to move objects with various masses at different speeds.
3. For every action, there is an equal and opposite reaction.

Recall that at the beginning of the 17th century, the general consensus was that light didn't have a speed, that it just appeared instantaneously, either present or not

During the 1600s this idea was seriously challenged. First, by Dutch scientist Isaac Beeckman in 1629, who set up a series of mirrors around a gunpowder explosions to see if observers noticed any difference in the when the flashes of light appeared.

Unfortunately for Beeckman and the progress of science, the results were inconclusive, but then in 1676 Danish astronomer Ole Rømer noticed strange variations in the eclipse times of one of Jupiter's moons over the course of a year.

Could this be because light took a longer time to travel from Jupiter when Earth was further away? Rømer thought so, and his rough calculations put the speed of light at about 220,000 kilometres per second – not a bad estimate at all, especially considering the data he would have had on planet sizes wasn't all that accurate.

Further experiments with beams of light on our own planet edged scientists closer to the right number, and then in the mid-1800s physicist James Clerk Maxwell introduced his Maxwell's equations – ways of measuring electric and magnetic fields in a vacuum.

Maxwell's equations fixed the electric and magnetic properties of empty space, and after noting that the speed of a massless electromagnetic radiation wave was very close to the supposed speed of light, Maxwell suggested they might match exactly.

It turns out Maxwell was right, and for the first time we could measure the speed of light based on other constants in the Universe.

At the same time, Maxwell's work strongly suggested that light was itself an electromagnetic wave, and after this idea was confirmed, it got picked up by Albert Einstein in 1905 as part of his theory of special relativity.

According to Einstein, in his 1949 book "Autobiographical Notes(opens in new tab)" (Open Court, 1999, Centennial Edition), the budding physicist began questioning the behavior of light when he was just 16 years old. In a thought experiment as a teenager, he wrote, he imagined chasing a beam of light.

Classical physics would imply that as the imaginary Einstein sped up to catch the light, the light wave would eventually come to a relative speed of zero — the man and the light would be moving at speed together, and he could see light as a frozen electromagnetic field. But, Einstein wrote, this contradicted work by another scientist, James Clerk Maxwell, whose equations required that electromagnetic waves always move at the same speed in a vacuum: 186,282 miles per second (300,000 kilometers per second).

Philosopher of physics John D. Norton challenged Einstein's story in his book "Einstein for Everyone" (Nullarbor Press, 2007), in part because as a 16-year-old, Einstein wouldn't yet have encountered Maxwell's equations. But because it appeared in Einstein's own memoir, the anecdote is still widely accepted.

If a person could, theoretically, catch up to a beam of light and see it frozen relative to their own motion, would physics as a whole have to change depending on a person's speed, and their vantage point?

Einstein recounted, he sought a unified theory that would make the rules of physics the same for everyone, everywhere, all the time.

This, wrote the physicist, led to his eventual musings on the theory of special relativity, which he broke down into another thought experiment: A person is standing next to a train track comparing observations of a lightning storm with a person inside the train. And because this is physics, of course, the train is moving nearly the speed of light.

Einstein imagined the train at a point on the track equally between two trees. If a bolt of lightning hit both trees at the same time, the person beside the track would see simultaneous strikes. But because they are moving toward one lightning bolt and away from the other, the person on the train would see the bolt ahead of the train first, and the bolt behind the train later.

Einstein concluded that simultaneity is not absolute, or in other words, that simultaneous events as seen by one observer could occur at different times from the perspective of another. It's not lightspeed that changes, he realized, but time itself that is relative. Time moves differently for objects in motion than for objects at rest. Meanwhile, the speed of light, as observed by anyone anywhere in the universe, moving or not moving, is always the same.

Today the speed of light, or c as it's commonly known, is considered the cornerstone of special relativity – unlike space and time, the speed of light is constant, independent of the observer.

What's more, this constant underpins much of what we understand about the Universe. It matches the speed of a gravitational wave, and yes, it's the same cthat's in the famous equation E=mc2.

E = mc^2 translates to "energy is equal to mass times the speed of light squared." In other words, wrote PBS Nova, energy (E) and mass (m) are interchangeable. They are, in fact, just different forms of the same thing.

But they're not easily exchanged. Because the speed of light is already an enormous number, and the equation demands that it be multiplied by itself (or squared) to become even larger, thus a small amount of mass contains a huge amount of energy. For example, PBS Nova explained, "If you could turn every one of the atoms in a paper clip into pure energy — leaving no mass whatsoever — the paper clip would yield [the equivalent energy of] 18 kilotons of TNT. That's roughly the size of the bomb that destroyed Hiroshima in 1945."

We don't just have the word of Maxwell and Einstein for what the speed of light is, though. Scientists have measured it by bouncing lasers back from objects and watching the way gravity acts on planets, and all these experiments come up with the same figure.

One of the many implications of Einstein's special relativity work is that time moves relative to the observer. An object in motion experiences time dilation, meaning that when an object is moving very fast it experiences time more slowly than when it is at rest.

When astronaut Scott Kelly spent nearly a year aboard the International Space Station starting in 2015, he was moving much faster than his twin brother, astronaut Mark Kelly, who spent the year on the planet's surface. Due to time dilation, Mark Kelly aged just a little faster than Scott — some "five milliseconds," according to the earth-bound twin. Since Scott wasn't moving near lightspeed, the actual difference in aging due to time dilation was negligible. In fact, considering how much stress and radiation the airborne twin experienced aboard the ISS, some would argue Scott Kelly increased his rate of aging.

But at speeds approaching the speed of light, the effects of time dilation could be much more apparent. Imagine a 15-year-old leaves her high school traveling at 99.5% of the speed of light for five years (from the teenage astronaut's perspective). When the 15-year-old got back to Earth, she would have aged those 5 years she spent traveling. Her classmates, however, would be 65 years old — 50 years would have passed on the much slower-moving planet.

We don't currently have the technology to travel anywhere near that speed. But with the precision of modern technology, time dilation does actually affect human engineering.

GPS devices work by calculating a position based on communication with at least three satellites in distant Earth orbits. Those satellites have to keep track of incredibly precise time in order to pinpoint a location on the planet, so they work based on atomic clocks. But because those atomic clocks are on board satellites that are constantly whizzing through space at 8,700 mph (14,000 km/h), special relativity means that they tick an extra 7 microseconds, or 7 millionths of a second, each day, according to American Physical Society publication Physics Central. In order to maintain pace with Earth clocks, atomic clocks on GPS satellites need to subtract 7 microseconds each day.

With additional effects from general relativity (Einstein's follow-up to special relativity that incorporates gravity), clocks closer to the center of a large gravitational mass like Earth tick more slowly than those farther away. That effect adds microseconds to each day on a GPS atomic clock, so in the end engineers subtract 7 microseconds and add 45 more back on. GPS clocks don't tick over to the next day until they have run a total of 38 microseconds longer than comparable clocks on Earth.

Special relativity and quantum mechanics are two of the most widely accepted models of how our universe works. But special relativity mostly pertains to extremely large distances, speeds and objects, uniting them in a "smooth" model of the universe. Events in special (and general) relativity are continuous and deterministic, wrote Corey Powell for The Guardian, which means that every action results in a direct, specific and local consequence. That's different from quantum mechanics, Powell continued: quantum physics are "chunky," with events occurring in jumps or "quantum leaps" that have probabilistic outcomes, not definite ones.

Researchers uniting special relativity and quantum mechanics — the smooth and the chunky, the very large and the very small — have come up with fields like relativistic quantum mechanics and, more recently, quantum field theory to better understand subatomic particles and their interactions.

Researchers striving to connect quantum mechanics and general relativity, on the other hand, consider it to be one of the great unsolved problems in physics. For decades, many viewed string theory to be the most promising area of research into a unified theory of all physics. Now, a host of additional theories exist. For example, one group proposes space-time loops to link the tiny, chunky quantum world with the wide relativistic universe.

However, the story doesn't quite end there, thanks to quantum theory, that branch of physics hinting that the Universe might not be quite as constant as we think.

Quantum field theory says that a vacuum is never really empty: it's filled with elementary particles, rapidly popping in and out of existence. These particles create electromagnetic ripples along the way, the hypothesis goes, and could potentially cause variations in the speed of light.

Studies into these ideas are ongoing, and we don't know for sure one way or the other yet. For now, the speed of light remains the same as it has for centuries, constant and fixed… but watch this space.

Today, the speed of light, or c as it's commonly known, is considered the cornerstone of special relativity – unlike space and time, the speed of light is constant, independent of the observer.

What's more, this constant underpins much of what we understand about the Universe. It matches the speed of a gravitational wave, and yes, it's the same cthat's in the famous equation E=mc2.

The Lorentz Invariance, named after Dutch physicist Hendrik Lorentz, holds that the laws of physics are the same for observers throughout the universe, no matter where they are or how fast they're moving.

The Lorentz Invariance is at the heart of special relativity, which predicts, among other things, that the speed of light in a vacuum is a constant 186,282 miles (299,791 kilometers) per second, whatever the situation.

This speed is indeed constant in all measurements to date, even those made at the highest energy levels that scientists can produce here on Earth with particle accelerators. And it holds at far higher energies as well, the kinds generated by dramatic astrophysical phenomena, a new study reports.

The study team analyzed data gathered by the High Altitude Water Cherenkov (HAWC) observatory, a system of 300 water tanks built on the shoulder of a volcano in the Mexican state of Puebla. Sensitive detectors inside these tanks measure the cascades of particles generated when high-energy gamma-rays strike the molecules in Earth's atmosphere.

The observatory has detected evidence of photons with energies above 100 teraelectronvolts — about 1 trillion times higher than the energy of visible light — streaming from at least four different astrophysical sources, reports the new study, which was published online Monday (March 30, 2019) in the journal Physical Review Letters.

That's a big deal, because it shows that even those supremely potent photons did not exceed the universal speed limit. If they had been moving faster than 186,282 miles per second, they would have decayed into lower-energy particles and never reached the water-tank detectors, study team members said.

We don't just have the word of Maxwell, Lorentz and Einstein for what the speed of light is, though. Scientists have measured it by bouncing lasers back from objects and watching the way gravity acts on planets, and all these experiments come up with the same figure.

Quantum theory hints that the Universe might not be quite as constant as we think.

Quantum field theory says that a vacuum is never really empty: it's filled with energetic virtual elementary particles, rapidly popping in and out of existence. These particles create electromagnetic ripples along the way, the hypothesis goes, and could potentially cause variations in the speed of light.

Studies into these ideas are ongoing, and we don't know for sure one way or the other yet. F

But for now, the speed of light remains the same as it has for centuries, constant and fixed.
Hartmann352

See: https://www.space.com/36273-theory-special-relativity.html

write4u

But for now, the speed of light remains the same as it has for centuries, constant and fixed.
Thanks for that excellent missive.
I am persuded that the speed of light remains constant and fixed and it indicates that at that at "c" a limit has been reached that cannot be broken.

So my question is why is there a limit at all and what is the significance of that particular value that cannot be exceeded under any circumstance, except perhaps during the inflationary epoch, when space and its mathematical constants were being created.

Question: did the inflationary epoch obey the the current spacetime limitations or did the baby universe actually expand at FTL during that brief moment in time?

If during the inflationary epoch space actually expanded at FTL what was it that allowed for this pre-quantum phenomenon?

Pentcho Valev

"The prison built by Einstein" is a euphemism. The blunt truth is that Einstein killed physics. The texts below imply that, if the speed of light is VARIABLE (it is!), modern physics, predicated on Einstein's 1905 constant-speed-of-light falsehood, is long dead (exists in a zombie state):

"He opened by explaining how Einstein's theory of relativity is the foundation of every other theory in modern physics and that the assumption that the speed of light is constant is the foundation of that theory. Thus a constant speed of light is embedded in all of modern physics and to propose a varying speed of light (VSL) is worse than swearing! It is like proposing a language without vowels." http://www.thegreatdebate.org.uk/VSLRevPrnt.html

"If there's one thing every schoolboy knows about Einstein and his theory of relativity, it is that the speed of light in vacuum is constant. No matter what the circumstances, light in vacuum travels at the same speed...The speed of light is the very keystone of physics, the seemingly sure foundation upon which every modern cosmological theory is built, the yardstick by which everything in the universe is measured...The constancy of the speed of light has been woven into the very fabric of physics, into the way physics equations are written, even into the notation used. Nowadays, to "vary" the speed of light is not even a swear word: It is simply not present in the vocabulary of physics." https://www.amazon.com/Faster-Than-Speed-Light-Speculation/dp/0738205257

"The whole of physics is predicated on the constancy of the speed of light...So we had to find ways to change the speed of light without wrecking the whole thing too much." https://motherboard.vice.com/en_us/article/8q87gk/light-speed-slowed

Hartmann352

Why does the universe have an upper speed limit on the speed of light? Why isn’t the top limit infinite? Or what if the speed of light was not constant but changed in different reference frames?

The speed of light is dependent on two fundamental properties of space, the vacuum permittivity and permeability. These are measured constants with no theory to explain them. These constants represent the resistance of space to the propagation of electromagnetic waves. Since space exhibits a resistance to electromagnetic (EM) wave propagation, this sets a finite limit to the speed of light. If this resistance was much lower or nonexistent, then the speed of light would be much faster, or perhaps infinite.

The physical significance of the speed of light is that it’s the upper limit of how fast information can flow. It is linked to causality and locality. If you are separated by some distance from an object, you cannot know anything about that object instantly.

If information could flow instantaneously from one part of the universe to another, it would mean that an event happening at any point in the universe could affect every other point. If there were a million hypernovae at any instant in space, this could kill us instantly because we would experience them simultaneously here on earth.

There would be no locality, which is the idea that objects in the universe are directly influenced only by their immediate surroundings.

Remember, the observable universe is simply a consequence of the fact that a) light has a finite speed and b) the universe has a finite age. So, we can only see so far. If you traveled to this 'edge', you would not notice anything peculiar. You would have your own observable universe, since you can also only see so far.

Another important concept to note is that the universe does NOT have an edge. As you say, it could be infinite. However, a finite universe also has no edge. It would be like the surface of a sphere, or a torus. You will eventually wrap around to your original position after traveling far enough.

The universe doesn't have an outside. It's self-contained, unlike the surface if the basketball. We say the surface of the basketball, a two dimensional sphere (a sphere is not to be confused with a ball, the three-dimensional inside of the basketball), is embedded in three-dimensional space. This is one type of geometry, in which you embed manifolds into other manifolds. This is the only type of geometry that the human brain can visualize, since everything around us is embedded in three dimensional space. Naturally, the universe must be a three dimensional manifold. Visualizing it would require you to image a four dimensional space to embed it into. You can't do this.

Einstein’s Special relativity guarantees that there is no such thing as simultaneity. How would this break causality?

Consider two events. If one observer determines that A caused B, a finite speed of light guarantees that all observers in all reference frames will also agree that A caused B, because in order for this not to be the case, information would have to travel back in time. In a universe with an infinite speed of light, observers would not be able to agree on the ordering of events, so there would be no agreement on causality.

We would have no sense of the history of the universe. There would be no redshift. We would not see the microwave background radiation, CMB. We would see the universe as it is in the current moment. But we would also see the full size of the universe, and know whether it was infinite or not.

The night sky would be completely lit up, because we would see all the light from all the stars everywhere in the universe simultaneously.

But an infinite speed of light would have a fundamental problem. If E=MC^2 is still correct, it would mean a universe with no mass, all energy. Since M = E/C^2. The higher the value of C, the more energy it takes to create mass. An infinite value of C would result in not being able to create any mass, regardless of how much energy we had. But note that E=MC^2 is based on Einstein’s special relativity, which is based on the idea that the speed of light is constant and finite, so this equation might not be valid.

Light speed is observer independent. You would measure the speed of light to be the same regardless of how fast you were traveling. How is that possible? Because time for the person traveling fast would run slower from the perspective of the person standing still.

This observer independence is necessary, otherwise there would not be a maximum speed limit because it would be different for different observers.

Varying speed of light would mean relativity is wrong and Quantum field theory would wrong. There would be no spacetime. Quantum mechanics may be salvageable. But causality would go out the window. The Big Bang would also have to be thrown out.

You may even have to bring back the idea of the luminiferous aether to explain how light moves according a fixed reference frame of the universe.

Why does the universe care about electromagnetic waves? Why is this speed of light so important in physics? What it cares about is causality, which is the maximum speed limit. And light just happens to have this maximum speed.

Because photons have no mass, they can travel with no restriction.

Another way to look at this maximum speed is to think about how how Space and time are equivalent in special relativity..

The conversion factor that unites space and time in our universe is the maximum speed of causality, the speed of light.

There is a sense in which space and time are interchangable, but there is also a very important sense in which they are distinct.

A corollary of special relativity is that, in effect, one person’s interval of space is another person’s interval of both time and space, and one person’s interval of time is also another person’s interval of both space and time. Thus, space and time are effectively interchangeable, and fundamentally the same thing (or at least two different sides of the same coin), an effect which becomes much more noticeable at relativistic speeds approaching the speed of light.

Einstein’s former mathematics professor, Hermann Minkowski*, was perhaps the first to note this effect (and perhaps understood it even better than Einstein himself), and it was he who coined the phrase “space-time” to describe the interchangeability of the four dimensions. In 1908, Minkowski offered a useful analogy to help explain how four-dimensionalspace-time can appear differently to two observers in our normal three-dimensional space. He described two observers viewing a three-dimensional object from different angles, and noting that, for example, the length and width can appear different from the different viewpoints, due to what we call perspective, even though the object is clearly one and the same in three dimensions.

 (Click for a larger version) The path taken by an object in both space and time is known as the space-time interval (Source: Wikibooks: http://en.wikibooks.org/wiki/ Special_Relativity/Spacetime)​

The idea perhaps becomes even clearer when we consider that our picture of the Moon is actually what the Moon was like 1¼ seconds ago (the time light takes to reach the Earth from the Moon), our picture of the Sun is actually how it looked 8½ minutes ago, and by the time we see an image of Alpha Centauri, our nearest star system, it is already 4.3 years out of date. We can therefore never know what the universe is like at this very instant, and the universe is clearly not a thing that extends just in space, but in space-time.

Einstein eventually identified the property of spacetime which is responsible for gravity as its curvature. Space and time in Einstein's universe are no longer flat (as implicitly assumed by Newton) but can pushed and pulled, stretched and warped by matter. Gravity feels strongest where spacetime is most curved, and it vanishes where spacetime is flat. This is the core of Einstein's theory of general relativity, which is often summed up in words as follows: "matter tells spacetime how to curve, and curved spacetime tells matter how to move". A standard way to illustrate this idea is to place a bowling ball (representing a massive object such as the sun) onto a stretched rubber sheet (representing spacetime). If a marble is placed onto the rubber sheet, it will roll toward the bowling ball, and may even be put into "orbit" around the bowling ball. This occurs, not because the smaller mass is "attracted" by a force emanating from the larger one, but because it is traveling along a surface which has been deformed by the presence of the larger mass. In the same way gravitation in Einstein's theory arises not as a force propagating through spacetime, but rather as a feature of spacetime itself. According to Einstein, your weight on earth is due to the fact that your body is traveling through warped spacetime!

Four-dimensional Minkowski spacetime is often pictured in the form of a two-dimensional lightcone diagram, with the horizontal axes representing "space" (x) and the vertical axis "time" (ct). The walls of the cone are defined by the evolution of a flash of light passing from the past (lower cone) to the future (upper cone) through the present (origin). All of physical reality is contained within this cone; the region outside ("elsewhere") is inaccessible because one would have to travel faster than light to reach it. The trajectories of all real objects lie along "worldlines" inside the cone (like the one shown here in red). The apparently static nature of this picture, in which history does not seem to "happen" but is rather "already there", has given writers and philosophers a new way to think about old ssues involving determinism and free will.

i

Due to the relativistic effects of time dilation, our idea of “now” is therefore something of a fictitious concept, one which we as humans have invented for ourselves, but for which nature itself has no real use. Physicists do not regard time as “passing” or “flowing” and time is not a sequence of events which happen: the past and the future are simply there, laid out as part of space-time. The "twins paradox" mentioned in the previous section can be considered an example of this: whereas the stay-at-home twin’s progress through space-time was wholly through time, the traveling twin’s progress was partly through space, so that his progress through time was less than that of the stay-at-home twin (so that he aged less).

Therefore, as Einstein remarked, “For us physicists, the distinction between past, present and future is only an illusion, however persistent”, and these concepts really do not figure at all in special relativity. Similarly, our whole conception of space becomes unreliable as the relativistic effects of length contraction become apparent at high relative speeds.

But the malleability and blurring of space and time also has implications for other aspects of physics. Just as Maxwell had shown that the electric and magnetic fields, once considered completely separate entities, were both just part of a single seamless entity known as the electromagnetic field, likewise (although perhaps more difficult to grasp and perhaps more unexpected) energy and mass turn out to be just different faces of the same coin, a connection encapsulated in Einstein’s justifiably famous formula, E = mc2.

In relativity (both flavours) we treat spacetime as a four dimensional manifold with three spatial dimensions and one time dimension - I'll explain the difference in a moment. Any observer can choose a set of coordinates with themselves at the origin, then they can measure out their three spatial axes with their ruler and measure their time axis with their clock.

But different observers won't agree on their axes. For example if I'm moving relative to you then your time axis will appear to me like a mixture of my time and space axes. So time and space are interchangeable in the sense that what looks like time to you looks like a mixture of time and space to me. If you're interested I talk about this some more in What is time, does it flow, and if so what defines its direction?. This mixing up of the time and space dimensions is behind phenomena like time dilation and Lorentz contraction.

However, while different observers won't agree on what constitutes space and what constitutes time, they will always agree that there are three spatial axes and one time axis. The difference is how these dimensions appear in the metic tensor.

Suppose we take good old Euclidean space and you move a distance 𝑑𝑥dx along the 𝑥x direction, 𝑑𝑦dyalong the 𝑦y direction and 𝑑𝑧dz along the 𝑧z direction. The total distance moved, 𝑑𝑠ds, is given by Pythagoras' theorem:
𝑑𝑠2=𝑑𝑥2+𝑑𝑦2+𝑑𝑧2ds2=dx2+dy2+dz2

In special relativity we have a similar total distance moved in 4D spacetime, and it's given by the metric:
𝑑𝑠2=−𝑐2𝑑𝑡2+𝑑𝑥2+𝑑𝑦2+𝑑𝑧2ds2=−c2dt2+dx2+dy2+dz2

But note that the time term 𝑑𝑡2dt2 appears in the equation with a negative value. This is the key difference between space and time. The spatial terms have a different sign to the time term. In that sense space and time are quite distinct.

Finally, that factor of 𝑐c is needed because when you add quantities they have to have the same units. So in the equation for the metric we cannot just add 𝑑𝑡2dt2 and 𝑑𝑥2dx2 because that would be adding seconds squared to metres squared. Multiplying by 𝑐c converts the units of time to be the same as the units of distance.

t=d

See: https://arvinash.com/why-isnt-the-speed-of-light-infinite/

See: https://physics.stackexchange.com/questions/334017/are-space-and-time-interchangeable

* Hermann Minkowski - on June 22, 1864, German mathematician Hermann Minkowski was born.

Minkowski developed the geometry of numbers and used geometrical methods to solve problems in number theory, mathematical physics, and the theory of relativity. But he is perhaps best known for his work in relativity, in which he showed in 1907 that his former student Albert Einstein’s special theory of relativity can be understood geometrically as a theory of four-dimensional space–time, since known as the “Minkowski spacetime“.
“The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.”
– Hermann Minkowski, Address to the 80th Assembly of German Natural Scientists and Physicians, (Sep 21, 1908)
Hermann Minkowski was born in Russia, but his family returned to Germany and settled in Königsberg when he was about eight years old. It became clear quite early, that he had great talents in mathematics. Minkowski started reading the works of Dedekind, Dirichlet, and Gauss during his school years in Königsberg and enrolled at the University of Königsberg in 1880. Minkowski received his doctorate in 1885 from Königsberg for a thesis titled “Untersuchungen über quadratische Formen, Bestimmung der Anzahl verschiedener Formen, welche ein gegebenes Genus enthält(studies of square forms, determination of the number of different forms that a given genus contains).

Minkowski’s interest in quadratic forms evolved early in his university studies. In 1881, Paris’ Academy of Sciences announced that the Grand Prix for mathematical science to be awarded in 1883 would be for a solution to the problem of the number of representations of an integer as the sum of five squares. Already in 1847, Eisenstein had given a formula for the number of such representations, but without a proof of the result.

At the age of 18, Minkowski reconstructed Eisenstein’s theory of quadratic forms and produced a beautiful solution to the Grand Prix problem. Henry John Stephen Smith had previously worked on the problem and also submitted his solution as well. The prize was then shared between these two mathematicians.

Starting from 1887, Minkowski spent a few years teaching in Bonn and Königsberg before being appointed to the Eidgenössische Polytechnikum Zürich. At Zurich Einstein was a student in several of the courses he gave and the two would later become interested in similar problems in relativity theory.[8] In 1902. Minkowski accepted a chair at the University of Göttingen, which was arranged by David Hilbert.[8] There, Minkowski became interested in mathematical physics gaining enthusiasm from Hilbert and his associates. He participated in a seminar on electron theory in 1905and he learnt the latest results and theories in electrodynamics.

From 1890 he developed his geometry of numbers which he had begun in his prize work and where he pioneered. His major work “Geometrie der Zahlen”Geometry of Numbers above appeared in 1896 and completed in 1910, developing and using methods of the theory of convex bodies and lattices and applying them to number theory. A central role was played by Minkowski ‘s lattice point theorem, with which he proved important theorems of algebraic number theory such as Dirichlet ‘s unit theorem or the finiteness of the class number. In 1907 his second major number theory work Diophantische Approximationen appeared, in which he gave applications of his geometry of numbers

Hermann Minkowski laid the mathematical foundation of the theory of relativity and developed an entirely new view of space and time. He made clear that Lorentz’ and Einstein’s work could be better understood in a non-euclidean space. Minkowski came to realize that space and time, which were previously thought to be independent, are coupled together in a four-dimensional ‘space-time continuum‘.

To his major works in the field belong ‘Raum und Zeit’ (Space and Time), published in 1907, as well as ‘Zwei Abhandlungen über die Grundgleichungen der Elektrodynamik(Two papers on the fundamental equations of electrodynamics) published two years later. Minkowski gave a sensational lecture on this in 1908 at the meeting of the Society of German Natural Scientists and Physicians. Einstein, who was initially opposed to Minkowski’s four-dimensional approach, later used his ideas on the space-time continuum in his general theory of relativity.

At the age of 44, Minkowski had an appendicitis. At that time, surgery to cure the disease was not yet common, but even surgery could not save his life. In the last hours he tried to complete numerous manuscripts. Hermann Minkowski died on January 12, 1909 in Göttingen.

See: http://scihi.org/hermann-minkowski-space-time/

See: https://einstein.stanford.edu/SPACETIME/spacetime2.html

Hermann Minkowski laid the mathematical foundation of the theory of relativity and developed an entirely new view of space and time. He made clear that Lorentz’ and Einstein’s work could be better understood in a non-euclidean space. Minkowski came to realize that space and time, which were previously thought to be independent, are coupled together in a four-dimensional ‘space-time continuum‘. Minkowski gave a sensational lecture on this in 1908 at the meeting of the Society of German Natural Scientists and Physicians. Einstein, who was initially opposed to Minkowski’s four-dimensional approach, later used his ideas on the space-time continuum in his general theory of relativity.
Hartmann352

write4u

If information could flow instantaneously from one part of the universe to another, it would mean that an event happening at any point in the universe could affect every other point. If there were a million hypernovae at any instant in space, this could kill us instantly because we would experience them simultaneously here on earth.
Yes, the question was not about the limit of propagation, but why is it exactly at 286,000 mph.

I understand the concept of resistance, but if the absolute speed limit of light in a vacuum is 286,000 mph then the amount of resistance must be calculable unless it is a function of quantum and it is impossible for qautum to occur faster than the speed of light.

If the universe , including light, is quantized then it seems to me that quantization itself also has an upper limit short else one ends up with smooth transition?

Mathematically, it refers to a property of solutions to the Schrödinger equation; since the Schrödinger equation is linear, any linear combination of solutions will also be a solution(s) .
...
Another example is a quantum logical qubit state, as used in quantum information processing, which is a quantum superposition of the "basis states" {\displaystyle |0\rangle }
and {\displaystyle |1\rangle }
. Here {\displaystyle |0\rangle }
is the Dirac notation for the quantum state that will always give the result 0 when converted to classical logic by a measurement.
Likewise {\displaystyle |1\rangle }
is the state that will always convert to 1. Contrary to a classical bit that can only be in the state corresponding to 0 or the state corresponding to 1, a qubit may be in a superposition of both states.
This means that the probabilities of measuring 0 or 1 for a qubit are in general neither 0.0 nor 1.0, and multiple measurements made on qubits in identical states will not always give the same result.

IOW. How fast does quantum change happen?

Hartmann352

From my above:

"The speed of light is dependent on two fundamental properties of space, the vacuum permittivity and permeability. These are measured constants with no theory to explain them. These constants represent the resistance of space to the propagation of electromagnetic waves. Since space exhibits a resistance to electromagnetic (EM) wave propagation, this sets a finite limit to the speed of light. If this resistance was much lower or nonexistent, then the speed of light would be much faster, or perhaps infinite.

An infinite value of C would result in not being able to create any mass, regardless of how much energy we had. But note that E=MC^2 is based on Einstein’s special relativity, which is based on the idea that the speed of light is constant and finite, so this equation might not be valid.

Light speed is observer independent. You would measure the speed of light to be the same regardless of how fast you were traveling. How is that possible? Because time for the person traveling fast would run slower from the perspective of the person standing still.

This observer independence is necessary, otherwise there would not be a maximum speed limit because it would be different for different observers.

Varying speed of light would mean relativity is wrong and Quantum field theory would wrong. There would be no spacetime. Quantum mechanics may be salvageable. But causality would go out the window. The Big Bang would also have to be thrown out.

Because photons have no mass, they can travel with no restriction."

There needed to be some sort of glue, some connection that allowed us to translate between movement in space and movement in time. In other words, we need to know how much one meter of space, for example, is worth in time. What's the exchange rate? Einstein found that there was a single constant, a certain speed, that could tell us how much space was equivalent to how much time, and vice versa.

Einstein's theories didn't say what that number was, but then he applied special relativity to the old equations of Maxwell and found that this conversion rate is exactly the speed of light.

Of course, this conversion rate, this fundamental constant that unifies space and time, doesn't know what an electromagnetic wave is, and it doesn't even really care. It's just some number, but it turns out that Maxwell had already calculated this number and discovered it without even knowing it. That's because all massless particles are able to travel at this speed, and since light is massless, it can travel at that speed. And so, the speed of light became an important cornerstone of modern physics.

But still, why that number, with that value, and not some other random number? Why did nature pick that one and no other? What's going on?

It has units after all: meters per second. And in physics any number that has units attached to it can have any old value it wants, because it means you have to define what the units are. For example, in order to express the speed of light in meters per second, first you need to decide what the heck a meter is and what the heck a second is. And so the definition of the speed of light is tied up with the definitions of length and time.

In physics, we're more concerned with constants that have no units or dimensions — in other words, constants that appear in our physical theories that are just plain numbers. These appear much more fundamental, because they don't depend on any other definition. Another way of saying it is that, if we were to meet some alien civilization, we would have no way of understanding their measurement of the speed of light, but when it comes to dimensionless constants, we can all agree. They're just numbers.

One such number is known as the fine structure constant, which is a combination of the speed of light, Planck's constant, and something known as the permittivity of free space. Its value is approximately 0.007. 0.007 what? Just 0.007. Like I said, it's just a number.

So on one hand, the speed of light can be whatever it wants to be, because it has units and we need to define the units. But on the other hand, the speed of light can't be anything other than exactly what it is, because if you were to change the speed of light, you would change the fine structure constant. But our universe has chosen the fine structure constant to be approximately 0.007, and nothing else. That is simply the universe we live in, and we get no choice about it at all. And since this is fixed and universal, the speed of light has to be exactly what it is.

In 1916 physicist Arnold Sommerfeld had a realization. If you modeled a hydrogen atom as Bohr did, but took the ratio of a ground-state electron's velocity and compared it to the speed of light, you'd get a very specific value, which Sommerfeld called α: the fine structure constant. This constant, once you folded into Bohr's equations properly, was able to precisely account for the energy difference between the coarse and fine structure predictions.

In terms of the other constants known at the time, α = e2/4πε0ħc, where:

• e is the electron's charge,
• ε0 is the electromagnetic constant for the permittivity of free space,
• ħ is Planck's constant,
• and c is the speed of light.
Unlike these other constants, which have units associated with them, α is a truly dimensionless constant, which means it is simply a pure number, with no units associated with it at all. While the speed of light might be different if you measure it in meters per second, feet per year, miles per hour, or any other unit, α always has the same value. For this reason, it's considered to be one of the fundamental constants that describes our Universe.

All we do know in both cases is that they are universal constants, and knowing their value is extremely useful. The situation with Pi is exactly analogous to that of 'c', and there are several other such universal constants. We know what the value of the constant is, but we don't know why they have the values they do.

Universal constants such as these are observed facts, not a consequence of any theory. As such they simply are what they are and we can make use of them without the neccessity of an underlying explanation for them.

See: https://www.forbes.com/sites/starts...stant-and-why-does-it-matter/?sh=3bccc35b4567

See: https://www.space.com/speed-of-light-properties-explained.html

The speed of light is determined by two fundamental physical constants, the magnetic permeability of free space and the electric permittivity of free space.

The laws of physics (specifically the equations that govern the electromagnetic field) imply that electromagnetic waves must always travel at a constant speed that can be calculated from these two constants.

That’s just the way the Universe works. If there is any underlying reason, we don’t know what it is.
Hartmann352

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write4u

That’s just the way the Universe works. If there is any underlying reason, we don’t know what it is.
So, we don't really know how the rate of quantum intervals?

Basically, I am asking if reality has a binary aspect, is reality expressed only half of the time?

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Hartmann352

We survive because reality may be nothing like we think it is.

Cognitive scientist Donald H. Hoffman asserts that not only do we invent our own personal views of reality, it’s an evolutionary necessity.

By Robby Berman

December 6, 2016

Professor of cognitive science at the University of California, Irvine Donald H. Hoffman, has doubts that reality is much like what we think it is. We live in a mental construction, he says, a sort of utilitarian fantasy, of our own devising. And it’s not a problem that it may not be a true representation of reality — in fact, it may be evolutionarily necessary.

His study, “Natural selection and veridical perceptions” concludes, among other things, that “perceptual information is shaped by natural selection to reflect utility, not to depict reality.”

Others, such as Alva Noë, declaring that our minds build our worlds. As Noë notes, what we see is light reflected off objects, not the objects themselves. Who knows what grass really looks like? We just know it’s something that absorbs all colors except green. When an object creates a fluctuation in air pressure that travels through that medium to our ears where it excites tiny fibers, we hear that fluctuation as a sound. We can think of both examples as merely the mechanics of how we see and hear, but the fact remains, we don’t directly perceive much.

The world we think we live in is a story based on experiences we’ve had with these and our other senses. And since we don’t see, say, electricity or WiFi signals, or colors or magnetic fields some other animals perceive, who knows what else is right under our noses? Logically, why would we assume that we see enough of reality to have a verdical understanding of it?

Hoffman himself draws his conclusion about reality largely from quantum mechanics, where systems are only defined once they’re observed. According to late physicist John Wheeler, “Useful as it is under ordinary circumstances to say that the world exists ‘out there’ independent of us, that view can no longer be upheld.” Hoffman laments that people working in neurology and philosophy of mind often deliberately ignore advances in quantum physics. He tells The Atlantic that, “They are certain that it’s got to be classical properties of neural activity, which exist independent of any observers—spiking rates, connection strengths at synapses, perhaps dynamical properties as well. These are all very classical notions under Newtonian physics, where time is absolute and objects exist absolutely. And then [the neuroscientists and philosophy of mind people] are mystified as to why they don’t make progress.”

The “Natural selection and verdical perceptions” study was an answer to those who assert that if we weren’t perceiving a real external reality, we’d have died out long ago. Hoffman’s position, and this is supported by his study, is that building a functional worldview is in fact a prerequisite to survival — an image of the world that keeps one alive is more important than one that’s objectively accurate. (If that’s even on the table.)

The constructions we invent may not be literally true, but still, he says of his own, “I’ve evolved these symbols to keep me alive, so I have to take them seriously. But it’s a logical flaw to think that if we have to take it seriously, we also have to take it literally.” Of what he identifies as a snake or a train, he says, “Snakes and trains, like the particles of physics, have no objective, observer-independent features. The snake I see is a description created by my sensory system to inform me of the fitness consequences of my actions.”

It’s worth pointing out that if there can be no “public” objects that aren’t personal constructions, science has a problem: “The idea that what we’re doing is measuring publicly accessible objects, the idea that objectivity results from the fact that you and I can measure the same object in the exact same situation and get the same results — it’s very clear from quantum mechanics that that idea has to go. Physics tells us that there are no public physical objects.” After all, “My snakes and trains are my mental representations; your snakes and trains are your mental representations.”

It’s not that Hoffman considers our constructed personal realities therefore worthless. In fact, they’re all we’ve got, and being real to us is a way of being true, after all. “I’m claiming that experiences are the real coin of the realm. The experiences of everyday life—my real feeling of a headache, my real taste of chocolate—that really is the ultimate nature of reality.” And it’s his and his alone.

See: https://bigthink.com/personal-growth/we-survive-because-reality-may-be-nothing-like-we-think-it-is/

See: https://www.sciencenews.org/century/quantum-physics-theory-revolution-reality-uncertainty

Quantum mechanics is the math that explains matter. It’s the theory for describing the physics of the microworld, where atoms and molecules interact to generate the world of human experience. And it’s at the heart of everything that made the century just past so dramatically unlike the century preceding it. From cell phones to supercomputers, DVDs to pdfs, quantum physics fueled the present-day electronics-based economy, transforming commerce, communication and entertainment.

But quantum theory taught scientists much more than how to make computer chips. It taught us that reality isn’t what it seems.

“The fundamental nature of reality could be radically different from our familiar world of objects moving around in space and interacting with each other,” physicist Sean Carroll suggested in a recent tweet. “We shouldn’t fool ourselves into mistaking the world as we experience it for the world as it really is.”

Everybody agrees that quantum physics has drastically remodeled humankind’s understanding of nature. In fact, a fair reading of history suggests that quantum theory is the most dramatic shift in science’s conception of reality since the ancient Greeks deposed mythological explanations of natural phenomena in favor of logic and reason. After all, quantum physics itself seems to defy logic and reason.

It doesn’t, of course. Quantum theory represents the ultimate outcome of logical reasoning, arriving at truths that could never be discovered merely by observing the visible world available to our eyes.

Matter’s basic particles are not little rock hard particles, but more like ghostly waves that maintain multiple possible futures until forced to assume the subatomic equivalent of substance. As a result, quantum math does not describe a relentless cause-and-effect sequence of events as Newtonian science had insisted. Instead quantum science morphs from dictator to oddsmaker; quantum math tells only probabilities for different possible outcomes. Some uncertainty in our perceived objects always remains.

Reality is what our all of senses working in concert perceive it to be, and my reality may not be yours.
Hartmann352

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