Space-Time Curvature & Quantum Field Theory

General Relativity is the name provided for Einstein's theory of gravity that was defined in Chapter 2 of my book. As the idea is usually shown, it explains gravity as a curvature in four-dimensional space-time. Now it is a concept far over and above the reach of common people. Just the concept of four-dimensional space-time causes the majority of us to shudder ... The answer in Quantum Field Theory is easy: Space is space and time is time, and there is no curvature. In QFT gravity is a quantum field in ordinary three-dimensional space, just like the other 3 force fields (EM, strong and weak).

This does not actually suggest that four-dimensional notation is not useful. It is a convenient way of handling the mathematical connection between space and time which is needed by special relativity. One could almost say that physicists couldn't live without having it. Still, spatial and temporal evolution are fundamentally different, and I say shame on people who aim to foist and push the four-dimensional concept onto the general public as vital to the understanding of theory of relativity.

The idea of space-time curvature likewise had its origin in mathematics. When seeking a mathematical approach that could embody his Principle of Equivalence, Einstein was led to the formulas of Riemannian geometry. And indeed, these formulas define four-dimensional curvature, for individuals who are able to imagine it. You see, mathematicians are not confined by physical constraints; equations that have a physical definition in 3 dimensions can possibly be generalized algebraically to any variety of dimensions. But when you do this, you are truly handling algebra (equations), not geometry (spatial configurations).

By expanding our minds, several of us are able to even make a faint mental image of what four-dimensional curvature might be like if it did exist. Nevertheless, claiming that the gravitational field equations are equal to curvature is definitely not the same as stating that there is curvature. In Quantum Field Theory, the gravitational field is just another force field, like the EM, strong and weak fields, though with a higher complication which is demonstrated in its higher spin value of 2.

While QFT resolves these paradoxical declarations, I really don't wish to leave you having the thought that the theory of quantum gravity is problem-free. While computational issues concerning the EM field were overcome with process referred to as renormalization, comparable challenges involving the quantum gravitational field have not been conquered. Fortunately they do not interfere with macroscopic computations, for which the QFT formulas become the same to Einstein's.

Your choice. Once again you the reader have an option, as you did in concern to the two methods to special relativity. The option is not about the formulas, it has to do with their perception. Einstein's equations can be deciphered as suggesting a curvature of space-time, unpicturable as it may be, or as detailing a quantum field in three-dimensional space, just like the other quantum force fields. To the physicist, it actually doesn't make much difference. Physicists are far more concerned with solving their formulas rather than with analyzing them. If you will permit me another Weinberg quote:

The important thing is to be able to make predictions about images on the astronomers photographic plates, frequencies of spectral lines, and so on, and it simply doesn't matter whether we ascribe these predictions to the physical effects of gravitational fields on the motion of planets and photons or to a curvature of space and time. (The reader should be warned that these views are heterodox and would meet with objections from many general relativists.)-- Steven Weinberg

Therefore in case you prefer, you can believe that gravitational effects are due to a curvature of space-time (despite the fact that you can't visualize it). Or, like Weinberg (and me), you can view gravity as a force field that, similar to the other force fields in Quantum Field Theory, exists in three-dimensional space and progresses in time according to the field equations.

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Why is the Speed of Light Constant?

The query "The reason is the speed of light constant?" is typically asked about by individuals attempting to learn physics. Google has 2760 links to that question. However the answer is so easy that a 10-year-old can understand it, that is, if you accept Quantum Field Theory.

Bring the ten-year-old to a lake and drop a rock in the water. Show her that the waves move through the water at a specific velocity, and tell her that this velocity depends solely on the properties of water. You may drop different items at different areas and show her that the waves go at the exact same rate, no matter the size of the object or location of the water.

Then tell her that sound travels through air with a fixed velocity that depends solely on the properties of air. You might wait for a thunderstorm and time the difference in between the lightning and the noise. Inform her that a whisper moves as fast as a scream. I believe a ten-year-old can perceive the concept that water and air have properties that establish the velocity of these waves, even if she does not understand the equations.

Any person who can understand this can then comprehend why the speed of light is constant. You see, in Quantum Field Theory space has properties, exactly as air and water have properties. These properties are known as fields.

As Nobel laureate Frank Wilczek wrote, "One of the most basic results of special relativity, that the speed of light is a limiting velocity for the propagation of any physical influence, makes the field concept almost inevitable.".

When you recognize the concept of fields (which of course is certainly not an easy one), that is really all you have to understand. Light is waves in the electromagnetic field that travel through space (not space-time) at a velocity governed by the properties of space. They abide by fairly basic formulas (not that you have to recognize them), just like sound and water waves follow basic formulas. OK, the Quantum Field Theory equations are a little bit more intricate, but quoting Wilczek again, "The move from a particle description to a field description will be especially fruitful if the fields obey simple equations ... Evidently, Nature has taken the opportunity to keep things relatively simple by using fields.".

Even so this inquiry can have a different meaning: "Why is the speed of light independent of motion?" This fact was first illustrated by the renowned Michelson-Morley experiment, in which light beams were measured as the earth revolved and rotated. The shocking result was actually that the speed of light was precisely the same no matter the earth's movement.

As I wrote in my publication (see quantum-field-theory. net): That the speed of light must be independent of movement was most surprising ... It makes no sense for a light beam - or anything, for that concern - to travel at the exact same speed regardless of the movement of the observer ... except if "something funny" is going on. The "something funny" ended up being much more astonishing than the M-M result itself. Essentially, objects contract when they move! More specifically, they contract in the direction of movement. Think about it. If the path length of Michelson's device in the forward direction contracted by the exact same amount as the extra distance the light beam would certainly have to travel due to motion, the two effects would cancel out. Indeed, this is the only way that Michelson's null result can be illustrated.

However the idea that objects contract when in motion was just as confusing as the Michelson-Morley outcome. Why should this be? Again the explanation is offered by Quantum Field Theory. Quoting once again from my publication:.

We need to recognize that even though the molecular configuration of an object appears to be stationary, the component fields are constantly interacting with one another. The EM field interacts with the matter fields and vice versa, the strong field interacts with the nucleon fields, etc. These interactions are what holds the object together. Now if the object is moving rather fast, this interaction between fields will certainly become more difficult because the fields, on the average, will need to interact through larger distances. Thus the object in motion ought to somehow adjust itself so that the identical interaction between fields can take place. How can it do this? The only way is by decreasing the distance the component fields need to travel. Since the spacing between atoms and molecules, and hence the dimensions of an item, are determined by the nature and arrangement of the force fields that bind them together, the dimensions of an object must therefore be affected by movement.

It is essential to recognize that it is not just Michelson's apparatus that contracted, it is anything and everything in the world, including Michelson himself. Even if the earth's speed and the consequent contraction were a lot greater, we on earth would continue to be ignorant of it. As John Bell discussed a moving observer:.

But will she not see that her meter sticks are contracted when laid out in the [direction of motion] - and even decontract when turned in the [other] direction? No, because the retina of her eye will also be contracted, so that just the same cells receive the image of the meter stick as if both stick and observer were at rest. - J. Bell (B2001, p. 68).

To conclude, for those who wish to comprehend physics, I say use Quantum Field Theory and: WAKE UP AND SMELL THE FIELDS.

EXACTLY WHAT DOES THE ELECTRON LOOK LIKE?

In June, 2014, I lectured at the Physics Department of the Czech Technical University in Prague. I began by asking the question "What does the electron look like?", and I presented 2 images. The first was the familiar Rutherford photo of particles orbiting a nucleus, and the 2nd was a (very simplified) photo of the electron as a field in the area surrounding the nucleus.

Then I wanted a vote. Rather remarkably only four people in the crowd chose the field photo, and not a single person picked the particle photo. In other words, THEY DID N'T KNOW. So here we are, 117 years after the electron was identified, and this highly educated group of physicists had no idea what it looks like.

Naturally when the electron was discovered by J. J. Thomson, it was naturally pictured as a particle. After all, particles are simple to imagine, while the field idea, let alone a quantized field, is not a very easy one to understand. But this photo soon ran into problems that led Niels Bohr in 1913 to offer that the particles in orbit image must be replaced by something new: undefined electron conditions that satisfy the following two postulates:

1. [They] have a peculiarly, mechanically unexplainable [emphasis added] stability.

2. In contradiction to the classical EM theory, no radiation takes place from the atom in the stationary states on their own, [however] a process of transition among two stationary states can be followed by the emission of EM radiation.

This led Louis de Broglie to suggest that the electron has wave properties. There then followed a sort of conflict, with Paul Dirac leading the "particle side" and Erwin Schrodinger the "wave side":.

We insist that the atom in truth is just the ... phenomenon of an electron wave captured, as it were, by the nucleus of the atom ... From the point of view of wave mechanics, the [particle image] would be just fictitious.-- E. Schrodinger.

Nevertheless the fact that a free electron acts like a particle could not be overcome, and so Schrodinger gave in and Quantum Mechanics became a theory of particles that are defined by probabilities.

A 2nd battle happened in 1948, when Richard Feynman and Julian Schwinger (along with Hideki Tomanaga) created various methods to the "renormalization" problem that plagued physics. Again the particle view espoused by Feynman triumphed, in huge part considering that his particle diagrams demonstrated simpler to deal with than Schwinger's field equations. So 2 generations of physicists have been brought up on Feynman designs and led to believe that nature is made from particles.

In the meantime, the theory of quantized fields was refined by Julian Schwinger:.

My retreat started at Brookhaven National Laboratory in the summer of 1949 ... Like the silicon chip of more recent years, the Feynman diagram was delivering computing to the masses ... But inevitably one has to bring it all together again, and then the piecemeal method loses a bit of its appeal ... Quantum field theory must work with [force] fields and [matter] fields on a completely equal ground ... Here was my challenge.-- J. Schwinger.

Schwinger's last variation of the theory was released between 1951 and 1954 in a collection of five documents entitled "The Theory of Quantized Fields". In his terms:.

It was to be the purpose of further developments of quantum mechanics that these 2 distinct timeless principles [particles and fields] are combined and become transcended in something that has no classical counterpart-- the quantized field that is a fresh conception of its very own, an unity that replaces the classical duality.-- J. Schwinger.

I believe that the primary reason these work of arts have been ignored is that many physicists considered them too tough to understand. (I know 1 who could not get past the very first page.).

Therefore the choice is all yours. You can believe that the electron is a particle, in spite of the many inconsistencies and absurdities, not to mention questions like how significant the particles are and what are they made of. Or you can believe it is a quantum of the electron field. The choice was described this way by Robert Oerter:.

Wave or particle? The answer: Both, and neither. You could consider the electron or the photon as a particle, but only if you wanted to let particles behave in the bizarre way illustrated by Feynman: appearing again, disrupting each other and canceling out. You can also think of it as a field, or wave, but you had to keep in mind that the detector always registers one electron, or none-- certainly never half an electron, no matter just how much the field has been split up or stretched out. Ultimately, is the field just a calculational instrument to tell you where the particle will be, or are the particles just calculational tools to tell you what the field values are? Take your pick.-- R. Oerter.

What Oerter neglected to mention is that QFT explains why the detector constantly registers one electron or none: the field is quantized. The Q in QFT is extremely important.

So when you choose, dear reader, I really hope you will not pick the image of nature that does not make sense-- that even its proponents call "bizarre". I wish that, like Schwinger, Weinberg, Wilczek, Hobson (and me), you will choose a truth made of quantum fields-- properties of space that are explained by the equations of QFT, the most philosophically appropriate picture of nature that I can think of.

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EINSTEIN DIDN'T SAY THAT!

Lots of people believe that Einstein's theory of general relativity states that gravity is due to curvature in fourth dimension. As an example, here's a recent question uploaded on Quora: ""Einstein tells us that gravity is motion in curved space-time, so why do scientists still refer to it a force?".

Forgive me for screaming, but this one truly makes me insane. EINSTEIN DID N'T SAY THAT! In his theory of general relativity, developed in 1915, gravity is a force field, somewhat different from the electro-magnetic (EM) field. It is NOT four-dimensional curvature. But first a bit of history.

The field idea was presented into physics in 1845 by Michael Faraday through his studies of electric and magnetic phenomena. When James Maxell generated formulas for Faraday's field in 1864, the field view of EM forces was commonly accepted. But Isaac Newton's theory of gravity, which consisted of "action at a distance", remained unchanged. Newton's theory was hugely successful, and is still taught in elementary physics programs at present, but Newton was not satisfied with the idea of "action-at-a-distance", saying "That one body may act upon another at a distance, through a vacuum, without the mediation of anything else ... is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it."

This altered, of course, when Einstein offered his principle of general relativity in 1915. In Einstein's words: "As a result of the more careful study of electromagnetic phenomena, we have come to regard action at a distance as a process impossible without the intervention of some intermediary medium ... The effects of gravitation also are regarded in an analogous manner ... The action of the earth on the stone takes place indirectly. The earth produces in its surroundings a gravitational field, which acts on the stone and produces its motion of fall ... [T] he intensity and direction of the field at points farther removed from the body are thence determined by the law which governs the properties in space of the gravitational fields themselves."...

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Looking at the Principle of Relativity the Easier Way

In the entire history of physics there is no equation more famous than e = mc2. This partnership amongst mass (m) and energy (e) was derived in 1905 by Albert Einstein from his Principle of Relativity. The derivation wasn't easy and warranted a paper by itself, referred to as "Does the inertia of a body depend upon its energy content?". The equation continues to baffle and dumbfound lay people, since in the usual particle picture of nature, it is difficult to see exactly why there is an equivalence between mass and energy.

In the meantime, a new theory called Quantum Field Theory was created. QFT was perfected in the 1950s by Julian Schwinger in 5 papers called "Theory of Quantized Fields". In QFT there are no particles, there are only fields-- quantized fields. Schwinger succeeded in placing matter fields (leptons and hadrons) on an equal footing with force fields (gravity, electromagnetic, strong and weak), despite the obvious differences among them. Moreover, Schwinger established the theory from fundamental axioms, as opposed to Richard Feynman's particle picture, which he justified because "it works". Regrettably it was Feynman who won the battle, and today Schwinger's method (and Schwinger himself) are mainly forgotten.

Yet QFT has lots of benefits. It has a stronger basis than the particle picture. It describes lots of things that the particle picture does not, including the numerous paradoxes connected with Relativity Theory and Quantum Mechanics, that have puzzled so many people. Philosophically, lots of people can accept fields as basic properties of space, instead of particles, whose composition is unknow. Or if there visualized as point particles, one can only ask "points of what?" And above all, QFT offers an easy derivation and understanding of e = mc2, as follows.

Mass. In classical physics, mass is a measure of the inertia of a body. In QFT some of the field equations contain a mass term that impacts the rate at which quanta of these fields evolve and propagate, slowing it down. Thus mass takes on the same inertial role in QFT that it does in classical physics. But this is not all it does; this exact same phrase causes the fields to oscillate, and the greater the mass, the higher the frequency of oscillation. The result, if you're imagining these fields as a color in space (as in my book "Fields of Color"), is a kind of glimmer, and the greater the mass, the quicker the glimmer. It might appear unusual that the same term that slows the spatial development of a field also provokes it to oscillate, but it is actually straightforward mathematics to show from the field equations that the frequency of oscillation is given by f = mc2/h, where h is Planck's constant.

Energy. In classical physics, energy means the capability to perform work, which is specified as applying a force over a distance. This definition, however, does not offer much of an image, so in classical physics, energy is a rather abstract idea. In QFT, on the other hand, the energy of a quantum is established by the oscillations in the field that comprises the quantum. In fact, Planck's famous relationship e = hf, where h is Planck's constant and f is frequency, found in the centennial year of 1900, follows directly from the equations of QFT.

Well, since both mass and energy are associated with oscillations in the field, it does not take an Einstein to see that there must be a connection between the two. In fact, any schoolboy can combine the two equations and find (big drum roll, please) e = mc2. Not only does the formula tumble right out of QFT, its significance can be imagined in the oscillation or "shimmer" of the fields. Nobel laureate Frank Wilczek calls these oscillations "a marvelous bit of poetry" that produce a "Music of the Grid" (Wilczek's phrase for space viewed as a lattice of points):.

"Instead of plucking a string, blowing through a reed, banging on a drumhead, or clanging a gong, we play the instrument that is empty space by plunking down different combos of quarks, gluons, electrons, photons, ... and let them settle till they get to balance with the spontaneous activity of Grid ... These resonances represent particles of different mass m. The masses of particles sound the Music of the Grid.".

This QFT derivation of e = mc2 is not typically known. In fact, I have never seen it in the books I've read. And still I consider it just one of the great accomplishments of QFT.

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Einstein and Newton Followed Similar Paths in Their Gravity Theories

When one looks at the paths that Newton and Einstein followed while pursuing their theories of gravity, one is struck by the many coincidences: the unexplained data on orbits, the sudden insight about falling objects, the need for a new mathematics, the calculational difficulties, the retroactive agreements, the controversy, the problem-plagued expeditions, and the final triumph and acclaim. Both men had worked in the same eccentric and lonely way, divorced from other scientists, armed with a great feeling of self-reliance while struggling with new concepts and difficult mathematics, and both produced earth-shaking results. One can’t help but wonder if these two greatest of scientists, born 237 years apart, were “relativistically related”, conceived as twins in some ethereal plane in a far-off galaxy and sent to earth to solve a matter of some gravity.

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Mass in Quantum Field Theory

The tale of exactly how the gravitational field entered into physics and quantum field theory is a remarkable one, entailing apples and moons, predictions and confirmations, problem-plagued expeditions, and the two greatest scientific geniuses of all time. And it might not have happened if not for the Great Plague.  Read more, Fields of Color - The Theory That Escaped Einstein