# Gravity: Newton or Einstein

Discussion in 'Physics & Math' started by Xmo1, Apr 27, 2017.

1. ### Xmo1Registered Senior Member

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So no graviton. We have curved spacetime. I'm confused ->. Talking about an RF transmitting antenna, or piece of Uranium, I think of radiation as being spherical. That is, no matter your position you will detect the radiation from the object, and it will be a uniform distribution. But I see particles, like in a cloud chamber have a definite direction. Onto gravity. I see the dimple from putting a ball on a piece of cloth, and how the cloth causes orbital movement. My thought is that spacetime is not like a piece of cloth. It has 3 dimensions. That is how gravitational lensing works. So given that spacetime is 3 dimensional, what does it really look like? Does the ball cause spacetime to be more dense near the surface of the ball, and less dense further away? Is it causing a dip or increase in the vacuum pressure? I'm getting (in my imagination) a picture of a ball that is pushing spacetime outward, causing it to be more dense near the surface of the ball. So I'm thinking Sun - Earth. If spacetime is actually denser near the Sun, why would Earth be attracted to the Sun. Is the orbit of Earth with its mass and speed interacting with differing spacetime densities?

Last edited: Apr 27, 2017

3. ### DaveC426913Valued Senior Member

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The random distribution of radiation will tend toward uniformity. It will become more uniform the more particles you detect.

Think of a machine gun spinning randomly on three axes. The first shot will go a particular direction; the next shot will go in some other particular direction. Over time - with hundreds and then thousands of shots, you will see a uniform spherical pattern.

Yes. Here is a 3-dimensional digram:

It may lead you down the wrong path thinking of a "density" of spacetime.

The lines that matter and particles travel when in a gravitational field are called geodesics. In spacetime they are actually straight (the shortest path between two points), and the particles follow those lines. This is why particles don't feel any sideways acceleration when falling into a gravity well: they're not actually changing direction.

5. ### rpennerFully WiredStaff Member

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One of the things that makes space similar to time is that it is metrical — it can be measured with numbers and physical units. So we talk about certain quantities of spatial separation (distance) and certain quantities of temporal separation (elapsed time), and these quantities add like numbers (or vectors). And vectors are implicit in algebraic descriptions of geometry which in the form of surveying has been dissecting space for profit for thousands of years.

But to talk about physics, Newton first came up with principles the motion of things obey.
First law:In an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.”
https://en.wikipedia.org/wiki/Newton's_laws_of_motion
Mathematically, Newton assumed space and time were different things, and developed the picture of motion from that and the Cartesian coordinate system, so "remaining at rest" and motion at "constant velocity" are both represented by the same mathematical constraint on velocity: $\frac{d \; }{dt} \vec{v}(t) = 0$
But velocity itself is defined as change in position (in an inertial coordinate system) per time so the purest Newtonian description of inertial motion is $\frac{d^2 \; }{dt^2} \vec{x}(t) = 0$.

Such an expression contains some philosophical baggage as time is the independent variable and position is a dependent variable with a functional relationship to time. It lends itself to a worldview of time being absolute because Newton assumed what was simultaneous for one admissible viewpoint would be simultaneous for all admissible viewpoints.

But in 1905, Einstein introduced some new ways to think about space and time, where the speed of light was constant but notions of simultaneity were not. In 1908, Minkowski described this as a geometry of space-time, and now space and time would have the same units (physicists choose to call 1/299792458 second as 1 meter so they may say the speed of light = 1, but if you want to keep both meters and seconds, then everywhere where I write t, assume I write "c times t" so the units work out right). How then to describe inertial motion if time is not absolute?

Mathematically, the a line in 4-dimensional space-time can be written a function of a single arbitrary parameter, giving x,y,z and t coordinates. There are an infinite number of ways to parameterize the same curve. Some parameters will be better than other in that some will give smooth motions simple descriptions and also have a metrical quality. For example if, $\frac{d^2 \; }{d \lambda^2} x(\lambda) = \frac{d^2 \; }{d \lambda^2} y(\lambda) = \frac{d^2 \; }{d \lambda^2} z(\lambda) = \frac{d^2 \; }{d \lambda^2} t(\lambda) = 0$ and $\frac{d \; }{d \lambda} t(\lambda) \neq 0$ then it follows that this represents a motion with constant coordinate velocity, exactly analogous to the Newtonian inertial motion.

So while infinite parameterizations exist for a given curve, only certain curves will have the property that they can be expressed as $\frac{d^2 \; }{d \lambda^2} x(\lambda) = \frac{d^2 \; }{d \lambda^2} y(\lambda) = \frac{d^2 \; }{d \lambda^2} z(\lambda) = \frac{d^2 \; }{d \lambda^2} t(\lambda) = 0$ and those we call straight lines.

Einstein's 1905 special relativity also constrains light and massive particles to $\left( \frac{d \; }{d \lambda} t(\lambda) \right)^2 \geq \left( \frac{d \; }{d \lambda} x(\lambda) \right)^2 + \left( \frac{d \; }{d \lambda} y(\lambda) \right)^2 + \left( \frac{d \; }{d \lambda} z(\lambda) \right)^2$ which is only an equality for light and massless phenomena. For massive particles we have the elapsed proper time which can be written as $\left( \frac{d \; }{d \lambda} \tau \right)^2 = \left( \frac{d \; }{d \lambda} t(\lambda) \right)^2 - \left( \frac{d \; }{d \lambda} x(\lambda) \right)^2 - \left( \frac{d \; }{d \lambda} y(\lambda) \right)^2 - \left( \frac{d \; }{d \lambda} z(\lambda) \right)^2$ which is a physically measurable metrical property of these space-time curves. For inertial motions, the relation between change in the arbitrary parameter λ and the elapsed proper time τ is a simple proportionality. For inertially moving clocks, elapsed proper time is metrical and is a good choice of parameterization. This "explains" why Newton's concept of universal absolute time was so successful for the physics of slow systems. He lacked the precision to measure the difference between elapsed proper time and the adopted convention of a particular coordinate time. Thus Newton's embrace of geometry stopped at the 3 dimensions of Euclid while Minkowski added a fourth.

So what is the superiority of arbitrary parameterization of the trajectories of particles in space-time? Firstly, it's simpler to apply a space-time coordinate transformation if the time coordinate isn't treated like an independent variable. Secondly, it generalizes to the case where the assumptions of Minkowski geometry don't exactly hold. I now speak of curved space-time.

In 1916, Einstein finished his theory of General Relativity for which I will ignore its use of arbitrary coordinate systems, gravity and dynamics to talk about just motion and curvature.
Where Minkowski (like Euclid and Descartes) was working with a constant geometry where
$\left( \frac{d \; }{d \lambda} \tau \right)^2 = +1 \left( \frac{d \; }{d \lambda} t(\lambda) \right)^2 + (-1) \left( \frac{d \; }{d \lambda} x(\lambda) \right)^2 + (-1) \left( \frac{d \; }{d \lambda} y(\lambda) \right)^2 + (-1) \left( \frac{d \; }{d \lambda} z(\lambda) \right)^2$
Einstein (following Riemann and others) introduced the ten functions of space-time called the symmetric space-time metric, which I will write out as if it was matrix multiplication.
$\left( \frac{d \; }{d \lambda} \tau \right)^2 = \begin{pmatrix} \frac{d \; }{d \lambda} t(\lambda) \\ \frac{d \; }{d \lambda} z(\lambda) \\ \frac{d \; }{d \lambda} y(\lambda) \\ \frac{d \; }{d \lambda} z(\lambda) \end{pmatrix}^{\textrm{T}} \begin{pmatrix} g_{tt}(t,x,y,z) & g_{tx}(t,x,y,z) & g_{ty}(t,x,y,z) & g_{tz}(t,x,y,z) \\ g_{xt}(t,x,y,z) = g_{tx}(t,x,y,z)& g_{xx}(t,x,y,z) & g_{xy}(t,x,y,z) & g_{xz}(t,x,y,z) \\ g_{yt}(t,x,y,z) = g_{ty}(t,x,y,z)& g_{yx}(t,x,y,z) = g_{xy}(t,x,y,z) & g_{yy}(t,x,y,z) & g_{yz}(t,x,y,z) \\ g_{zt}(t,x,y,z) = g_{tz}(t,x,y,z) & g_{zx}(t,x,y,z) = g_{xz}(t,x,y,z) & g_{zy}(t,x,y,z) = g_{yz}(t,x,y,z) & g_{zz}(t,x,y,z) \end{pmatrix} \begin{pmatrix} \frac{d \; }{d \lambda} t(\lambda) \\ \frac{d \; }{d \lambda} z(\lambda) \\ \frac{d \; }{d \lambda} y(\lambda) \\ \frac{d \; }{d \lambda} z(\lambda) \end{pmatrix}$

Did this complicate things? Yes. In practice that's way too many symbols to keep straight, so Einstein abbreviated notation in a robust manner and we would normally write the above as $d \tau^2 = g_{\alpha \beta} \, d X^{\alpha} \, d X^{\beta} , \quad g_{\alpha \beta} = g_{\beta \alpha}$ but that's just too big a leap to make from Newton in a single post.

Given that all the notions of geometry are now in the symmetric space-time metric, we can use it, its "matrix inverse" and its derivatives to compute the connection between coordinate derivatives and geometrically meaningful derivatives. So the $\frac{d^2 \; }{d \lambda^2} x(\lambda) = \frac{d^2 \; }{d \lambda^2} y(\lambda) = \frac{d^2 \; }{d \lambda^2} z(\lambda) = \frac{d^2 \; }{d \lambda^2} t(\lambda) = 0$ of 1905 becomes:
$\frac{d^2 \; }{d \lambda^2} x(\lambda) + \Gamma_{\alpha \beta}^x \, dX^{\alpha} \, dX^{\beta} = 0 \\ \frac{d^2 \; }{d \lambda^2} y(\lambda) + \Gamma_{\alpha \beta}^y \, dX^{\alpha} \, dX^{\beta} = 0 \\ \frac{d^2 \; }{d \lambda^2} z(\lambda) + \Gamma_{\alpha \beta}^z \, dX^{\alpha} \, dX^{\beta} = 0 \\ \frac{d^2 \; }{d \lambda^2} t(\lambda) + \Gamma_{\alpha \beta}^t \, dX^{\alpha} \, dX^{\beta} = 0$

Alas, my attempt to introduce these connection coefficients got bogged down in 1) there are lots of them, 2) they can't be written out in terms of the metric easily as matrix operations, 3) my main point is that we have replaced the straight lines of Minkowski geometry with the geodesic lines of curved space time. Geometry is king in 1916 General Relativity.

https://en.wikipedia.org/wiki/Chris...of_the_second_kind_.28symmetric_definition.29
https://en.wikipedia.org/wiki/Geodesics_in_general_relativity#Mathematical_expression

Being able to compute the "straight lines" for a given geometry is some of the easier maths of General Relativity. Far harder is proving a given space-time satisfies Einstein's equations. Harder still is finding a solution more complicated than the simplest, most symmetrical examples. But we can approximate solutions well and this has in every case upheld the predications of Einstein over Newton, not just in gravity but in motion itself.

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7. ### danshawenValued Senior Member

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EM radiation (from a radio/microwave transmit antenna or a light bulb) follows the inverse square law (speherical). Gravitational fields, and also gravity waves, also follow the inverse square law, but gravity waves are more akin to acoustic (sound) waves (in "empty" space) as opposed to EM radiation.

"Spacetime" as proposed by Minkowski and Special Relativity, treats time mathematically as though it were a fourth physical dimension proportional to propagation of the speed of light, as rpenner has demonstrated.

In a cloud chamber, ionization/condensation trails of subatomic and or radioactivity decay products present as straight line trajectories. Most of those particles present as discrete quanta of energy packets, including, but not limited to, helium nuclei, neutrons, and electrons or x-rays. This is not the same as the EM spectrum, but some of the particles may have comparable energies.

Last edited: Apr 28, 2017
8. ### Xmo1Registered Senior Member

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Would you say that the planet/mass(?) is a gravity well? Getting pretty fuzzy on this end. Let me read further comments.

Last edited: Apr 29, 2017
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9. ### Q-reeusValued Senior Member

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Except for at least one major shortcoming. Sound waves in a fluid are purely longitudinal p waves. GR's GW's are purely transverse shear (s) waves. Even if one tries to think of space as a kind of 'solid', acoustic waves are necessarily both p and s in such (owing to anything corresponding to an analogue of actual GW sources e.g. binary compact masses).

Last edited: Apr 29, 2017
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10. ### Xmo1Registered Senior Member

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I know what gravity is. What is spacetime? What is it made of?

11. ### Xmo1Registered Senior Member

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check.
So it expands, it bends, but no one knows what it is (it is not a particle, a cloud, an element), spacetime? Ok, weakalidia, and I hope they don't have the same thing as rpenner.

Week says spacetime is a mathematical model. So it doesn't exist? Um, no. It exists. So what is it made of?

Last edited: Apr 29, 2017
12. ### The GodValued Senior Member

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Space exploration is not some absurd or purely academic exercise, this has practical implications.

I sincerely do not know (and I can vouch none here would know) how GR maths is used in GPS and how only and only GR could do whilr none others (Gravitational time dilation at altitude can be compensated simply by invoking the newtonian potential energy difference between surface and altitude, no GR is needed).

All other trajectory calculations etc involve Newtonian. In fact GR cannot solve even 2- body problem without extreme complexity issues or approximations.

So at least I will not go with Einstein on gravity.

13. ### danshawenValued Senior Member

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No one here, nor Newton, nor Einstein, knows what the cause of gravity is. If they did know the cause of gravity, they would not need to use a proportionality constant (the universal gravitational constant), or be able to relate how to derive it from more elementary principles or components.

Spacetime is a mathematical construct consisting of three (geometric, Euclidean) physical dimensions, combined with a fourth dimension proportional to light travel time which unlike the other three physical dimensions, is contrived by means of complex mathematics with a built-in arrow to preclude the possibility of backward movement in time. This spacetime construct seems to work fine to describe Special Relativity's Lorentz contraction (or 4D Minkowski rotation) of the physical dimension of space in the direction of relative motion, and also of Lorentz time dilation (no particular direction) between frames of reference in relative motion with respect to each other. The construct requires the speed of light in a vacuum to be a Lorentz invariant quanitity that measures the same irrespective of relative motion.

Irrespective of the limitations of any of the foregoing constructs, spacetime itself evidently is comprised only of energy transfer events and the quantum field(s) that support the dynamics of those events.

Last edited: Apr 29, 2017
14. ### danshawenValued Senior Member

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The graviton is / was a boson that is a theoretical construct of the Standard Model of particle physics. It explains gravitation in terms of a force pair exchange of gravitons. The model acknowledges that forces of any kind always occur in balanced pairs by means of an exchange of appropriate bosons. The model works for EM, electroweak, and strong nuclear atomic forces. However a graviton may never be seen experimentally in an atomic collider due to the design having no practical means for accelerating anything not possessing an electric charge. The graviton is not predicted to possess an electric charge.

15. ### danshawenValued Senior Member

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There is power in knowing what inertia is. For Newton, it explained how planets orbited the sun. For Einstein, it yielded both E=mc^2 and a prediction of the precession of the perihelion of the planet Mercury. For CERN's LHC, it led to the discovery of the Higgs boson, which provides inertial mass to itself, quarks, electrons, electroweak bosons, neutrinos, and their antiparticles.

Without the Higgs term in the Lagrangian that describes all of the force pairs interacting within atomic structure, the entire structure unravels into so much unbound energy and propagates in spherical radiation fashion into the surrounding quantum foam.

It is impossible for a particle to provide another particle with inertia without getting inertia back. Force only occurs in pairs, and Newton's third law has never been broken. There is power in knowing what inertia is. Don't call this "classical". Greeks and their ancient geometry were classical.

16. ### danshawenValued Senior Member

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Although I understand there is some basis for thinking of empty space surrounding gravitating bodies as having the property of curvature, the curvature described is not completely analogous to curvature of a three dimensional solid. There has always existed both rotational and translational forms of inertia in all frames of reference and at all scales, but it is a mistake to suppose that a fixed position in space exists or has ever existed, or to refer to something as curvature which in certain frames of reference, is not curvature at all. There is no origin for a geometrical coordinate system that makes sense for doing geometry in inertialess space unless it is related to a center of rotation for a discrete particle.

Favoring a mathematical or other description of one frame of reference over another betrays a bias of a preferred frame of reference. In terms of a bias that has any binding to reality, there is no such physical thing.

Time dilation that is the result of relative motion exists in "reality" because when the traveling twin returns, the ages can be compared and they are different. Length contraction in the direction of motion has no such property, and so that "contraction", or Minkowsky "4D rotation", as well as an relative increase in inertial mass, is something restricted to a single physical direction, and is observable only while relative motion in that single direction persists.

It is the same for space curvature. Space can have inertia that is evidently related to rotation or a lack thereof, but when or if the rotation on any scale stops, space itself is neither rotating nor curved. If it were not for the fact that the Higgs quantum field exists everywhere in space and was not spinning, space itself would possess no physical reality. Without the Higgs mechanism in atomic structure to mark its passage at different rates at rest or in relative motion, neither would time.

There is power in understanding what inertia is.

Last edited: Apr 29, 2017
17. ### Xmo1Registered Senior Member

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Bravo danshawen. That's the closest I've read to a definition of spacetime.

18. ### danshawenValued Senior Member

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I want you to know, the responses I gave would not have been marginally possible without the guidance and scrutiny provided gratis from a multitude of others on this forum, including and especially rpenner.

19. ### Xmo1Registered Senior Member

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Thank you. This is going to provide me a jump off point to getting a more solid understanding of some of the concepts of physics, including gravity and spacetime. As a note, I'm one of those people who learned that Newtonian gravity was the way to go, so (as old as it might be) understanding (getting a really solid grasp of) the new physics (I bought the book) is muddling with that, and requires me to 'get over it' to learn and understand the new model. I don't do this full time either, so it's a stretch for me. Thanks again.

Last edited: Apr 29, 2017
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20. ### Xmo1Registered Senior Member

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Acknowledged with respect to rpenner and yourself.

21. ### rpennerFully WiredStaff Member

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Physics isn't about telling you about what things are, but rather about giving precise communicable frameworks for predicting the behavior of a large class of observable phenomena.

Gravity is a phenomena, described differently in Newton's Universal Gravitation and Einstein's General Relativity. Einstein's predictions of observable effects of gravitation turn out to be more precise than Newton's.

What spacetime "is" is a question in metaphysics. Physics doesn't care what spacetime is "made of" unless and until those constituents are shown to have related observable phenomena associated with them. What spacetime is to physics is a metrical environment so that events don't all happen at the same time and the same place. Newton assumed "same time" was for everyone the same 3-d slice, while Einstein (1905) assumed it was different 3-d slices which were a function of which inertial motion one adopted as a standard of rest, while Einstein (1916) assumed that "same time" was the locus of all geodesics passing though an event where the initial coordinate time derivative was zero. Newton assumed "same place" was a trajectory with no x-, y- or z-velocity, Einstein(1905) assumed it was a time-like straight line, Einstein (1916) assumed it was a time-like geodesic. None of these views tells you what spacetime "is" but only how it is predicted to behave. Einstein (1905) spacetime has length contraction, time dilation and a limiting speed which Newton's doesn't have. Einstein (1916) spacetime has geodesics which don't remain parallel, attractive gravity, tidal effects, gravitational waves, gravitational time dilation which neither Newton or Einstein (1905) had.

There are speculative hypotheses of how spacetime might be modeled as having as-yet-unevidenced constituents and thus some as-yet-undiscovered observable phenomena not accounted for in Einstein (1916) but even if they were uniquely supported by observation they would at best explain what spacetime "is" in terms of "more fundamental entities" and ultimately tell you nothing about what those fundamental entities "are". That's the nature of the infinite descent of "why" questions — ultimately we run aground on the shores of human ignorance because physics can't tell you about reality, but only about the behavior of phenomena we observe.

This division between reality and what we can know of reality has been philosophically distinguished for thousands of years. See Plato's Allegory of the Cave: https://en.wikipedia.org/wiki/Allegory_of_the_Cave

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22. ### Xmo1Registered Senior Member

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I am not going to mention particle physics, which at it's core does seem to define sub-atomic particles. How can you talk about time without first defining it? I can look in the dictionary, but essentially it is an amorphous phenomena? Spacetime is metaphysical? I understand your point about the why well, but seems we are walking on way too much quicksand if there is not a more concrete reality involved with a bunch of these phenomena. Is there a time particle, or is this simply a way to provide a framework for discussion of things we don't understand? There is now, with Higgs, a model of physics that describes most of the universe in at least the mathematical terms of physics. I'm saying so that you know I am aware of it. Shouldn't there now be concrete definitions of some of these things (like time, and spacetime), so that we don't need to call them phenomena anymore? There probably is, but I am not aware of them. If I had to imagine what you might say, it would be, "There is. It's right there in the math," and I must confess you are probably right. Rpenner, you've been around for awhile, and you seem to know physics better than 99 percent of us, so I think I'm going to start reading your posts. Thank you for your work here.

Last edited: Apr 29, 2017
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23. ### danshawenValued Senior Member

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There should be answers, yes, but more complete ones are unlikely until every facet of a new discovery like the Higgs has been examined and reconciled to existing frameworks of physics knowledge known to work, or to work in limited fashion. This is what I did not completely understand when I started here. You cannot completely repudiate Minkowski's formulation of spacetime, for example, without a framework to replace it that explains more than it did.

Patience is a virtue. There is power in understanding what rotational, translational, and restricted dimensional inertia is, and also what it means for free space to have an inertial component that is a composite of these kinds. The uncertainty principle means no more or no less than a fixed position of space with inertia does. If a light bulb doesn't come on brightly at this point, don't worry. Getting over a flat Earth has inertia of its own, mostly rooted in Euclidean geometry.