Having just joined the forum some of you will groan that I have brought this up again but I can't find the answer just by surfing around. So here goes with the question. I am almost prepared to accept that gravity is not a force as Newton thought but it is the result of warped space-time. Thus the earth creates a "well" in space because of and proportional to its mass. The moon orbits the earth trapped in the "well" but because of its speed it remains in orbit and doesn't crash down to earth. OK so far. Now my question doesn't refer to orbiting bodies but to earth bound objects. How does the warping of space explain why I don't just float off into space. Why did Newton's apple fall to eath. For me, a force is still involved. When the apple fell it accelerated at "g" because F=mg where F is the force of gravity not curved space. Any answers please?

A force is, most definitely, involved. In relativity, gravity is described as a warping of spacetime... but it is only an analogy that should not be taken too far. It is a conceptual idea to help you understand how Einstein's field equations work. Space is not a physical, material thing that warps. Space is just distance between objects.

The problem comes from the pedantic way physicists say that gravity is not a force. In fact it is a force which on the macro scale of planentary motion the force warps space time but on the smaller scale of men on earth the force attracts the two objects together. Have I stated my own grand unification theory.

The problem comes from the pedantic way physicists say that gravity is not a force.

Which physicists say this?

Stephen Hawking in his book " A brief history of time ".

The problem comes from the pedantic way physicists say that gravity is not a force. In fact it is a force which on the macro scale of planentary motion the force warps space time but on the smaller scale of men on earth the force attracts the two objects together. Have I stated my own grand unification theory.

Careful - not one real physicist would EVER say that gravity is not a force!! Along with the electromagnetic, weak and strong nuclear forces, it is one of the basics. And the goal of the GUT is combine all of them.

Your question about the Moon circling the gravity well of the EARTH should have answered it for you - you are inside that gravity well and it's effects are just as apparent on you as on the moon. :)

Stephen Hawking in his book " A brief history of time ".

I don't recall reading that.

In fact it is a force which on the macro scale of planentary motion the force warps space time but on the smaller scale of men on earth the force attracts the two objects together. Have I stated my own grand unification theory.

I don't think the scale of a man is small enough to change the idea of warping space-time. In fact, the scale that the spacetime picture fails is much smaller than even an atom---it is the planck scale.

Apples and planets both move along geodesics in space-time. This is the basic idea. I should explain a few things here, and if you already know this, then I'll just waste the bandwidth.

If you've ever looked at the routes that airlines travel in the back of the magazine on an airplane, you'll notice that none of the lines are straight:

http://www.usairways.com/common/resources/_images/aboutus/pressroom/y_g_int_map.jpg

But you should have learned somewhere that the shortest (and quickest) distance between two points is a straight line. So are the air carriers of the world conspiring to make people late? No---they are travelling along the most efficient routes. On a curved surface, the shortest distance between two points is a great circle, and when projected onto a flat surface, the lines aren't straight anymore. On a geneal curved surface, these things are called geodesics.

Now, space-time is a curved surface. Matter and energy is bound to that surface, and quite generally we can argue that an object in freefall must travel along a geodesic. Why? Minimization of energy.

So the apple, when travelling in the earth's space-time, travels along a geodesic. That geodesic carries it towards the center of the earth. The planets exist in stable orbits about the sun's gravity well, and the moons about the planets.

Which physicists say this?
Einstein, I believe. To make Newton's laws work in a non-inertial frame one must invent "fictitious forces" such as the centrifugal "force" and the Coriolis effect. All such fictitious forces have one thing in common: The "force" on an object is in some way proportional to the object's mass.

One such fictitious force is the apparent acceleration that results when the observer is fixed in an accelerating reference frame. Suppose our observer is in an enclosed elevator room that has no windows. Suppose further that the room is attached to an rocket accelerating at 1g in deep space (far from any gravitational bodies). Now suppose the observer releases an apple. He will see it accelerate to the floor of the room.

Let's now change the circumstances: Fix the room to the surface of the Earth. Our observer sees exactly the apple behave exactly the same as in the accelerating rocket scenario. There is no way for the observer to determine if he is an accelerating room or a fixed room subject to some external gravitational "force".

This is Einstein's equivalence principle. There is no way to distinguish the fictitious force caused an accelerating reference frame and the "force" caused by gravity. In general relativity, gravity is a fictitious force rather than a "real" force.

Well, I've just never heard gravity demoted like that :) Admittedly, I haven't studied GR very closely. When we treat gravity on a microscopic scale, we generally treat it just like any other force, it's just mediated by a spin two particle instead of a spin one particle. (To be fair, the force that holds protons and neutrons together is mediated by spin 0 particles.)

This is Einstein's equivalence principle. There is no way to distinguish the fictitious force caused an accelerating reference frame and the "force" caused by gravity. In general relativity, gravity is a fictitious force rather than a "real" force.

I don't know...it all soudns like symantics to me.

I think the original conceptual idea of Einstein behind GR was that gravity is not force. But once you derived the equations you can still treat gravity as a force that follows the equations. If I remember correctly, tensor gravity theory with background Minkowski space-time will give you exactly the same consequences as GR. So it is a matter of interpretation I guess, like there are many interpretations of quantum mechanics.

I think the original conceptual idea of Einstein behind GR was that gravity is not force. But once you derived the equations you can still treat gravity as a force that follows the equations. If I remember correctly, tensor gravity theory with background Minkowski space-time will give you exactly the same consequences as GR. So it is a matter of interpretation I guess, like there are many interpretations of quantum mechanics. well said. I can remember correctly that gravity is still one of the fundamental interactions of nature, after electromagnetic and the rest.

I think the original conceptual idea of Einstein behind GR was that gravity is not force. But once you derived the equations you can still treat gravity as a force that follows the equations. If I remember correctly, tensor gravity theory with background Minkowski space-time will give you exactly the same consequences as GR. So it is a matter of interpretation I guess, like there are many interpretations of quantum mechanics.
Which theory are you speaking about, temur?? GR is a tensor gravity theory by my understanding. It uses a metric tensor to describe the 'shape' of spacetime, a curvature represented by the Riemann curvature tensor.

There are many gravity theories. The Brans-Dicke theory adds a scalar field to physically change the gravitational constant from place to place, but spacetime is still modelled as curved. These are the scalar-tensor theories.

Kaluza-Klein theories use a five dimensional spacetime instead of GR's four, but still models gravity as curved spacetime.

Yang-Mills theories model gravity in Euclidean 4-dimensional spacetime, but they are guage theories instead of tensor theories. Guage theories seem to be easier to unify with quantum mechanics. Quantum Chromodynamics is a guage theory, as is the work-in-progress quantum field theory.

Kaluza-Klein theories use a five dimensional spacetime instead of GR's four, but still models gravity as curved spacetime.

We should be very careful!!! GR is NOT a four dimensional theory! GR in five dimensions can be shown to give you a Kaluza Klein theory, but there is nothing that prevents GR from existing in arbitrary dimensions.

Yang-Mills theories model gravity in Euclidean 4-dimensional spacetime, but they are guage theories instead of tensor theories. Guage theories seem to be easier to unify with quantum mechanics. Quantum Chromodynamics is a guage theory, as is the work-in-progress quantum field theory.

Again, there's nothing preventing one from writing down a gauge theory in five or two or ten dimensions. Also, QFT is more of a way to solve Yang-Mills theories perturbbatively.

If you've ever looked at the routes that airlines travel in the back of the magazine on an airplane, you'll notice that none of the lines are straight:

perhaps that is just for the graphic.:)

perhaps that is just for the graphic.:)

No, airline routes really are curved. The distance between 2 points on a sphere is actually shorter if you follow a curved path as illustrated above. I would guess that the curves in the picture are a bit exaggerated, though I could be wrong.

http://en.wikipedia.org/wiki/Great_circle_distance

Which theory are you speaking about, temur?? GR is a tensor gravity theory by my understanding. Eh? What precisely is a "tensor theory"? Or maybe - what exactly is "tensor gravity"? This makes no sense.It uses a metric tensor to describe the 'shape' of spacetime, a curvature represented by the Riemann curvature tensor. Would you care to go into this in some mathematical detail? I can't make sense of it, as presented. Are you sure that this is not web-surf babble?

No, airline routes really are curved. The distance between 2 points on a sphere is actually shorter if you follow a curved path as illustrated above. I would guess that the curves in the picture are a bit exaggerated, though I could be wrong.

http://en.wikipedia.org/wiki/Great_circle_distance

Well yeah, but it depends on how far your going.:D

Eh? What precisely is a "tensor theory"? Or maybe - what exactly is "tensor gravity"? This makes no sense.Would you care to go into this in some mathematical detail? I can't make sense of it, as presented. Are you sure that this is not web-surf babble?

I like Charles Francis' explanation of general covariance:

The Principle of General Covariance

Definition: An equation is covariant if it has the same form in any coordinates, up to the naming of coordinate axes.

The general principle of relativity states Local laws of physics are the same irrespective of the coordinate system used to quantify them. Vectors are not invariant, as their coordinate representation changes with the coordinate system. Relationships between vectors, defined from the dot product, are unchanged by coordinate transformation. Such relationships are said to be covariant. Similarly, relationships between tensors are covariant. The form of the general principle of relativity most directly applicable to classical physics is the principle of general covariance,

The equations of physics have tensorial form.

http://www.teleconnection.info/rqg/IntroductionToTensors

Well yeah, but it depends on how far your going.:D

No. The path is always curved.

No. The path is always curved.

Ahhh lovely relativity -- what is locally flat may be globally curved. :)

Please explain why you make this assertion. The general theory of manifolds may allow it, in a rather loose sense, but say what you mean by "curved" in this context. Otherwise, without some supporting mathematics, this is an empty assertion. (I warn you all, the evidence for this is quite terrifying)

Umm, the spacetime interval is different than that given by the Pythagorean theorem? ex: ds != sqrt(dx1*dx1 + dx2*dx2 + ... + dxn*dxn)

I'm not even sure who you're talking to, and I'm not sure if this "answer" matches your question, but I thought I'd give it a shot. :)

Ahhh lovely relativity -- what is locally flat may be globally curved. :)

Yes, but you also don't even have to invoke realtivity in this case. Because there are some people that don't know the difference between "level" and "flat." ;) :D

BenTheMan,
We should be very careful!!! GR is NOT a four dimensional theory! GR in five dimensions can be shown to give you a Kaluza Klein theory, but there is nothing that prevents GR from existing in arbitrary dimensions.
Yes, General Relativity is a four dimensional theory. It unifies space and time in a four dimensional manifold called spacetime. When you use a five dimensional manifold (with a compactified fifth dimension) it is know as Kaluza-Klein theory. I have not read of a theory based on GR that has 10 or 11 dimensions. What are such theories called?
Again, there's nothing preventing one from writing down a gauge theory in five or two or ten dimensions.
That may be true, but I only mentioned Yang Mills theory as a gravitational theory framework in four dimensional Euclidean (flat) spacetime. Aren't higher-dimensional guage theories known as vierbein theories?

Quarkhead,
Eh? What precisely is a "tensor theory"? Or maybe - what exactly is "tensor gravity"? This makes no sense.
I repeated timur's 'tensor gravity theory' phrase which is a correct term to describe GR. GR can also be called a metric theory of gravity.
Would you care to go into this in some mathematical detail? I can't make sense of it, as presented. Are you sure that this is not web-surf babble?
No, I am not a mathematician nor do I wish to learn the maths. I only know a little science philosophy, which I did learn on the web. I can give you a link to an explanation of the Riemann curvature tensor, but it is probably over your head. James R is about the only member here with good understanding of GR maths. The link:
http://en.wikipedia.org/wiki/Riemann_tensor

Quarkhead, nor do I wish to learn the maths. This is your choice, obviously (and your loss, in my opinion) But in that case such ex cathedra pronouncements as thisBenTheMan, Yes, General Relativity is a four dimensional theory. might be deemed a little unwise. Einstein's field equations do not specify any particular dimension, as you could easily see if you looked at them. It is true that Einstein himself modelled spacetime as a 4-manifold, but the field equations work as well for any n-dimensional manifold, just as Ben said.

As for this: I can give you a link to an explanation of the Riemann curvature tensor, but it is probably over your head.You don't see this as a tad, just a tad patronizing? You may assume that I am the best judge of what is over my head, not you. Twit.

And, astonishing as it may seem, I, like all here, have access to the internet, even to Wikipedia - amazing isn't it! I don't need your links, I can find them myself, if need be. As it happens, though it's irrelevant, I do not need Wikipedia to tell me about the Riemann tensor.

As for this: You don't see this as a tad, just a tad patronizing?

I thought so too.

Considering you're the one who created a thread on manifolds, I figured you knew what curvature was and that you were just seeing who was full of B.S. and who wasn't. :)

me,
“ I can give you a link to an explanation of the Riemann curvature tensor, but it is probably over your head. ”

quarkhead,
You don't see this as a tad, just a tad patronizing? You may assume that I am the best judge of what is over my head, not you. Twit.
It may be, but the 'patronizing' manner was in response to this patronizing post by you:
Eh? What precisely is a "tensor theory"? Or maybe - what exactly is "tensor gravity"? This makes no sense. I can't make sense of it, as presented. Are you sure that this is not web-surf babble?

As far as 'my' speculation that GR may be over your head, I was drawing that conclusion from what you said in your manifold thread:
temur made this suggestion:
Another way would be to go to the Riemannian manifolds, curvature, connection etc.
your response was:
Sure, but I don't really understand the mathematics there. If you can help us out, that would be great!

I do not know mathematics, but I do know your thread was mostly about using point-set topologies to model your manifold. I may be mistaken, but I thought your thread was about modeling locally Euclidean spaces on a manifold. GR uses a subset of Riemannian manifolds called pseudo-Riemannian manifolds, or lorentzian maniflods. Lorentzian manifolds are locally modeled on Minkowski space.

OK, sure, whatever......

Eh? What precisely is a "tensor theory"? Or maybe - what exactly is "tensor gravity"? This makes no sense.

I think what (s)he means (whether (s)he knows it or not) is that the graviton of GR transforms as a tensor under the Lorentz group SO(3,1).

Yes, General Relativity is a four dimensional theory. It unifies space and time in a four dimensional manifold called spacetime. When you use a five dimensional manifold (with a compactified fifth dimension) it is know as Kaluza-Klein theory. I have not read of a theory based on GR that has 10 or 11 dimensions. What are such theories called?

Absolutely not. QuarkHead is precisely correct when he says that Einstein's equations can be written down for any n-dimensional manifold. For example, there is a very interesting class of solutions to Einstein's equaitons called deSitter and Anti-deSitter (dS and AdS). 5 dimensional AdS space is very important to string theory, for example.

Further, you are confused about what a Kaluza-Klein theory IS---a Kaluza-Klein theory is a theory that has compact dimensions. For example, people have worked out the details of six dimensional Kaluza-Klein theories.

String theory lives in a ten dimensional background, described by Einstein's equations, and M-theory lives in an eleven dimensional background.

Considering you're the one who created a thread on manifolds, I figured you knew what curvature was and that you were just seeing who was full of B.S. and who wasn't.

I haven't seen any hallmark contriutions from you...

BenTheMan,
Absolutely not. QuarkHead is precisely correct when he says that Einstein's equations can be written down for any n-dimensional manifold. For example, there is a very interesting class of solutions to Einstein's equaitons called deSitter and Anti-deSitter (dS and AdS). 5 dimensional AdS space is very important to string theory, for example.
First off, Ben, the following question is not meant to be a 'challange' or argument directed at you, but an attempt to understand on my part. All I know is the very basics of the various string theories and M-theory.

What I cannot understand is how any of the string theories, or M-theory, can be 'based on' General Relativity, or fully compatible with GR. They are compatible with QM and the standard model, of course. The reason I cannot understand how they are compatible is because of the graviton. The graviton is a force-carrying particle that mediates the gravitational force in QM, string theories, and quantum field theories, but does not appear in GR if I understand correctly. In GR, mass warps (curves) 4-dimensional spacetime and is not a force. GR modeled gravity in geometrical manner because forces normally act on objects according to their mass. Objects in a vacuum will follow the same trajectory when acted on by gravity whether they are as light as a feather or as heavy as an asteroid. So, how is a force-carrying graviton compatible with a theory in which gravity is not a force? How fast do these gravitons travel, the speed of light? If they travel at exactly the speed of light, are they subject to such things as the Shapiro Delay and gravitational lensing which affect the arrival times of photons? The Shapiro Delay is when photons 'take longer' to transverse an area including a gravitational field than they do if no gravitational field is present. If gravitons are unaffected by gravity fields, then they could transit a distance between two points faster than photons. If gravity can bend the graviton's trajectory, or delay the graviton's transit times, how do gravitons escape the event horizon of a black hole? Sorry about so many questions, but such things pop into my head when I consider the details.

By the way, I am a 61 year old retired male.

2inquisitive---

Your question deserves a long and detailed answer. I am on my way back to Columbus, Ohio, and am just about to get on the road (I spend the night in Bumfuck, Tennessee).

I will start a thread outlining the differences/similarities between the theories.

By the way, I am a 28 year old grad student in physics at the Ohio State University.

spin 0 particlesA spin 0 particle is a geometrical notion. A particle, say a lepton, has a very small (zero) spatiality, an electron looks mathematically, like a point charge. Spin is to do with degrees of freedom.

A 2d substrate can have a well, a plane, a wire or a dot etched into it. Wells are a 3d space electrons can bounce around in. A 2d plane has two degrees, a wire has one, and a dot has zero. A spin zero particle has n+1 degrees of freedom: two alternate spins, up and down. This is only ever a relative state of affairs.

P.S. This is a general observation (not reflected back at anyone here, necessarily)..

P.P.S. A single photon is also an informational model; if a photon propogates through a certain kind of crystal, it can divide into two bits, each exactly half the information (energy), and spin is conserved: where the original had spin-up+spin-down, each entangled photon has the opposite spin of its partner, algebraically, and the two spins add to the unitary state of the first. Something like that.

I haven't seen any hallmark contriutions from you...

Try reading my work once in a while, and your opinion might change. I even do a full dimensional analysis, because I know you sometimes have issues with that.

I was paying QuarkHead a compliment, so simmer down.

I do not know mathematics, but I do know your thread was mostly about using point-set topologies to model your manifold. I may be mistaken, but I thought your thread was about modeling locally Euclidean spaces on a manifold. GR uses a subset of Riemannian manifolds called pseudo-Riemannian manifolds, or lorentzian maniflods. Lorentzian manifolds are locally modeled on Minkowski space.

Minor correction: Topologically, every manifold is locally modeled on Euclidean space. Quarkhead's thread was about smooth manifolds, which include both Riemannian and pseudo-Riemannian manifolds (but on the other hand on any smooth manifold there exist many Riemannian metrics, but there is no reason to pick one as special). The distinction between Riemannian and pseudo-Riemannian manifolds shows up only when you introduce a metric on the (smooth) manifold.


So, how is a force-carrying graviton compatible with a theory in which gravity is not a force? [...] If gravity can bend the graviton's trajectory, or delay the graviton's transit times, how do gravitons escape the event horizon of a black hole?

I am not an expert, but let me give a try. In GR gravity is conceptually not force but nothing can stop you from interpreting gravity as a force in GR, a force that is governed by the Einstein field equations. So if you somehow can show that the Einstein equations are a special case of the general field equations in whatever theory you are considering, then you can say that your theory includes GR as a special case. You can even say that gravity is a force in your theory and in macroscopic scale this force appears as if it is induced by the curvature because your theory satisfies some (perhaps quantum) form of general covariance.

About the graviton escaping the event horizon, there are always virtual gravitons that can "travel" instantaneously. It is the same mechanism that electrically charged black holes can interact with other charges electromagnetically.

A spin zero particle has n+1 degrees of freedom: two alternate spins, up and down. This is only ever a relative state of affairs.

This is not correct. ``Spin'' classifies how a particle transforms (as a representation of) the Lorentz group.

So, how is a force-carrying graviton compatible with a theory in which gravity is not a force?

I think temur did a pretty good job answering your question.

I would add that Einstein's equations and Maxwell's equations are classical equations, and so they don't really know about gravitons and photons, respectively.* It may help to think of things in this way: in electrodynamics, everything is given to you in terms of a vector potential A and a scalar potential phi. These two things give you the electric and magnetic fields. When you make electrodynamics manifestly Lorentz invariant, you have a single object, A_\mu. This is a tensor of rank one. Likewise, in GR (which is already manifestly covariant) you have an object called the metric, g_{\mu\nu}.

When you quantize electrodynamics (a la Feynman), the rank one tensor turns into a spin one photon. Presumably, when we quantize gravity, the rank two metric will turn into a spin two graviton.

*I did mispeak (slightly) earlier, when I said ``...the graviton of GR...''. GR doesn't contain a graviton per se, just like electrodynamics doesn't contain a photon. If you get upset when you read this last bit about EM not having a photon, remember that Maxwell only knew about electromagnetic radiation.

OK, thanks temur and Ben.

So, I suppose what ya'll are saying is that since GR doesn't address how mass curves spacetime at the quantum level, it is deemed OK, at least by superstring/QFT theorists, to use the force-mediating graviton.

The 'virtual' gravitons carry momentum that leads to the gravitational attraction between the mass inside the event horizon and a particle outside the event horizon, correct? If I understand correctly, in simple terms the momentum carried by the virtual graviton can manifest itself on the 'opposite' side of the exterior particle, pushing the particle toward the singularity. If the virtual graviton acts instanteously, how does it 'know' how much force (momentum) to transfer? By this, I mean gravity falls off by the inverse square ratio, so the virtual graviton would need to lessen the amount of momentum transferred by the same inverse square/distance ratio, correct? How does that explain non-massive particles such as photons being trapped in the accretion disk near the event horizon? Can the virtual graviton connect with, and transfer momentum to photons as well? If virtual gravitons mediate the gravitational force, are all gravitons 'virtual' and travel instanteously or at least faster than light? I mean if virtual gravitons do the same job as 'real' gravitons, why would you need two types?

Virtual gravitons would be used to calculate gravitational attraction between two bodies, but real gravitons would constitute gravitational waves. Massive object would feel force under the influence of gravitational wave even though there is no massive body nearby that can immediately be accounted for the gravitational influence.

On the other hand, we should be careful about virtual gravitons since this is introduced in analogy to virtual photons and virtual photons are just one way of calculating things. Correct me if I am wrong, but there is no way to know virtual photons really exist or it is simply a convenient calculational tool, otherwise they would not be virtual. It may happen that the virtual graviton thing does not work at all in a well tested theory of quantum gravity.

A spin zero particle has n+1 degrees of freedom: two alternate spins, up and down. This is only ever a relative state of affairs.
”
This is not correct. ``Spin'' classifies how a particle transforms (as a representation of) the Lorentz group.Not correct? How many spin states can a spin 0 particle have then? I thought it was n+1. Electrons can have 3/2 spin states, 'cause they're a spin 1/2 particle.
That's a single photon or electron, ensembles are more complicated.

A photon has two degrees of freedom because a one-dimensional spin can go up or down (or left or right), but only two directions are allowed for a single degree of freedom. For a 1/2 spin particle, there are 3/2 degrees, or three out of two, which is like three legs of a parallelogram because 2 degrees give 4 possible directions, two bidirectional dimensions of spin, geometrically speaking.

Not correct? How many spin states can a spin 0 particle have then? I thought it was n+1. Electrons can have 3/2 spin states, 'cause they're a spin 1/2 particle.
That's a single photon or electron, ensembles are more complicated.

It's not quite that easy. For a massive particle, there are 2n+1 states---these correspond to spin states for a fermion, and ``polarizations'' for a boson. For a massless particle, I can't remember how exactly the counting goes.

A photon has two degrees of freedom because a one-dimensional spin can go up or down (or left or right), but only two directions are allowed for a single degree of freedom.

Then why do massive bosons, like the W and Z bosons, have 3 polarizations? They are also spin one.

2inquisitive---

Check out this webpage by John Baez.
http://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html
I think it answers many of your questions more succinctly that I ever could :)

Hi Guys

I cannot believe how far off topic this thread has got, for me at least. I got the answer to my original question in the first few replies which was that we stay attached to the earth because we are inside the space time curvature caused by the mass of the earth. However what now needs to be answered is "why does mass/energy curve space time?". The gravitons theory may work at the sub atomic level but what about at planetary level. I'm sorry my questions are a bit simply stated but it sometimes does you particle physiscists good to stop talking about spins and bosons and Higgs particles and just concentrate on the question.

Presumably, when we quantize gravity, the rank two metric will turn into a spin two graviton.Just to be naughty: can you give any reason why you think gravity should be quantizable? there is the aesthetic argument, of course - Mother Nature's Laws must be reconcilable at all scales, which doesn't really wash, and which smacks of Intelligent Design at worst.

Is there some a priori reason to believe that gravity should be quantizable? Any data, that is, that already says that GR is not a complete description of the gravitational field and its effects?

And is there any reason, other than the two distasteful (to me) arguments above that says that there need ever be a unification of physical laws at the micro and macro scale?

I quote Wolfgang Pauli (in paraphrase of the Anglican marriage ceremony):

What God has torn asunder, let no Man join!!

Hi Guys

I cannot believe how far off topic this thread has got, for me at least. I got the answer to my original question in the first few replies which was that we stay attached to the earth because we are inside the space time curvature caused by the mass of the earth. However what now needs to be answered is "why does mass/energy curve space time?".
GR doesn't address the question of 'why' or how mass/energy curves spacetime. GR models the effects of gravity by using geodesics to describe the paths objects will take in the presence of mass. In GR, masses do not gravitationally interact directly with each other. Mass/energy interacts directly with spacetime only, affecting the path another object will take through the curved spacetime.

The 'why' and 'how' question of how gravity possibly 'works' is what is being discussed by the 'particle physicists', so they are not off topic unless you want a GR-only answer to your question. But, as I said, GR doesn't address the mechanism by which mass/energy interacts with spacetime, or what spacetime is 'made of', if anything.

Virtual gravitons would be used to calculate gravitational attraction between two bodies, but real gravitons would constitute gravitational waves. Massive object would feel force under the influence of gravitational wave even though there is no massive body nearby that can immediately be accounted for the gravitational influence.
OK, so virtual gravitons produce an attractive force that is responsible for satellites, and the moon, orbiting the Earth and real gravitons that travel at the speed of light are components of a gravitational wave, correct? So 'gravity' is a force that acts instantaneously, or at least faster than light, by the actions of virtual gravitons in guantum theory, correct? Is gravity modeled as a stationary field surrounding a mass? In GR, gravitational waves are only produced by a disturbance to a massive object, causing a 'ripple' to travel through spacetime at the speed of light.

In current thinking, does the quantization of gravity stand to explain why it is such a hugely weak force as opposed to the other fundamental forces?

In current thinking, does the quantization of gravity stand to explain why it is such a hugely weak force as opposed to the other fundamental forces?

Maybe. This is called the hierarchy problem (http://en.wikipedia.org/wiki/Hierarchy_problem). Essentially, the higgs mass is very small (100 GeV) compared to the Planck Scale (10^19 GeV). In nature, anytime we see huge differences in scales like this, there's typically a reason. All fo the solutions to the hierarchy problem that I know of are low energy physics (i.e., physics around 100 GeV) instead of high energy (planck scale) solutions.

Just to be naughty: can you give any reason why you think gravity should be quantizable? there is the aesthetic argument, of course - Mother Nature's Laws must be reconcilable at all scales, which doesn't really wash, and which smacks of Intelligent Design at worst.

Is there some a priori reason to believe that gravity should be quantizable? Any data, that is, that already says that GR is not a complete description of the gravitational field and its effects?

And is there any reason, other than the two distasteful (to me) arguments above that says that there need ever be a unification of physical laws at the micro and macro scale?

I quote Wolfgang Pauli (in paraphrase of the Anglican marriage ceremony):

What God has torn asunder, let no Man join!!


Well...let's suppose for a second that you DIDN'T believe in black holes, despite all evidence for their existence. You still have all of the observational evidence that the universe tends to a very hot, very dense initial state. Then you have to ask, does gravity still exist in this very hot, very dense state, and you have to say yes. The problem is, GR doesn't work in such an environment.

So now you have a problem---observation predicts something that is outside the abilities of the theory to describe. That means that there must be some dynamics which prevent such a state from occuring in Nature, which means your theory is STILL incomplete. So nothing is REALLY gained from this.

For me, it is quite odd that gravity should be different from any of the other forces in nature. Why should gravity be described as curvature, when every other force we have is understood in terms of Feynman diagrams and virtual force carriers?

OK, so virtual gravitons produce an attractive force that is responsible for satellites, and the moon, orbiting the Earth and real gravitons that travel at the speed of light are components of a gravitational wave, correct? So 'gravity' is a force that acts instantaneously, or at least faster than light, by the actions of virtual gravitons in guantum theory, correct? Is gravity modeled as a stationary field surrounding a mass? In GR, gravitational waves are only produced by a disturbance to a massive object, causing a 'ripple' to travel through spacetime at the speed of light.

Now we are reaching the limit of my rough understanding. I believe that any interaction is instanteneous quantum mechanically, but we cannot use this to send classical information faster than light. Virtual gravitons may go faster than light, but after averaging (or whatever people do in quantum field theory) you will see gravity acts with speed of light. (It has something to do with the commutator of observables vanishing outside the light cone,I think Ben could explain it more clearly.)

GR doesn't address the question of 'why' or how mass/energy curves spacetime. GR models the effects of gravity by using geodesics to describe the paths objects will take in the presence of mass. In GR, masses do not gravitationally interact directly with each other. Mass/energy interacts directly with spacetime only, affecting the path another object will take through the curved spacetime.

The 'why' and 'how' question of how gravity possibly 'works' is what is being discussed by the 'particle physicists', so they are not off topic unless you want a GR-only answer to your question. But, as I said, GR doesn't address the mechanism by which mass/energy interacts with spacetime, or what spacetime is 'made of', if anything.

Thanks for this reply, you and me are roughly the same age and I seem to be on your wave length more than the others. The younger posters are indulging themselves in a very interesting discussion but it's way over my head. I'm surpised however at the differing opinions on the fundamentals like the spin state of a photon.

how does einsteins spacebending theory explain planets' elliptical orbits? space does not curve elliptically, so shouldn't the orbits be round?

how does einsteins spacebending theory explain planets' elliptical orbits? space does not curve elliptically, so shouldn't the orbits be round?
It works much the same as Newtonian gravity in a weak gravity field, such as the gravitational potential around a planet or star. If a particle were 'dropped' into the gravity field at the correct velocity for the gravitational potential at the location, the particle's orbit would be a circle. But if a particle enters a gravitational field at a too high a velocity, the particle either will not be captured in orbit, or will enter an ellipital orbit. Don't forget, a Newtonian gravity field also predicts the same gravitational potential (force) at a set radius, say 100 miles, from the center of the gravitating mass.

Newtonian gravity is said to give inaccurate results in strong gravitational fields, such as around a neutron star or black hole. Newtonian gravity predicts orbital velocities for massive objects can exceed the speed of light near the event horizon of a black hole.

I'm surpised however at the differing opinions on the fundamentals like the spin state of a photon.

Some opinions are more well-informed than others.

A force is, most definitely, involved. In relativity, gravity is described as a warping of spacetime... but it is only an analogy that should not be taken too far. It is a conceptual idea to help you understand how Einstein's field equations work. Space is not a physical, material thing that warps. Space is just distance between objects.

Space is a physical material thing that warps. For distance to exist there has to be this "thing."

MetaKron---

Do you know what you are talking about or are you just posting results from google searches?

What happened to the extra pages on this thread

What happened to the extra pages on this thread

http://www.sciforums.com/showthread.php?t=76326

BenTheman, I take it you are the moderator of this board. I posted several times that this thread was veering well off topic from my original question. Thanks for cleaning it up.

Just to be naughty: can you give any reason why you think gravity should be quantizable? there is the aesthetic argument, of course - Mother Nature's Laws must be reconcilable at all scales, which doesn't really wash, and which smacks of Intelligent Design at worst.

Is there some a priori reason to believe that gravity should be quantizable? Any data, that is, that already says that GR is not a complete description of the gravitational field and its effects?

And is there any reason, other than the two distasteful (to me) arguments above that says that there need ever be a unification of physical laws at the micro and macro scale?

I quote Wolfgang Pauli (in paraphrase of the Anglican marriage ceremony):

What God has torn asunder, let no Man join!!

Gravity is geometry. The main cause of spacetime flux is called momentum and the stress energy. These coupled with a few geometric equations gives a relativley simple layout of how much spacetime will bent and how strong the gravitational field will be.

The original idea from Einstein was that Newton said if the sun suddenly vanished then all the planets instantaneously would drift off into space. Einstein saw that his own theory of special relativity did not allow this (nothing can travel FTL (faster than light). Thus this is how the general theory aroused.

If you need to know any more about spacetime feel free to ask :D.

SV Wimer: Thanks for getting this thread back on track. My problem is understanding how curved space-time keeps objects on the ground back here on earth. The answer I got very early on in this thread was that we are inside the curvature of space-time caused by the mass of the earth. This is OK but I wonder if you had a better explanation.

The original idea from Einstein was that Newton said if the sun suddenly vanished then all the planets instantaneously would drift off into space.So spacetime is about the Sun vanishing?

What's momentum got to do with it, or this stress you mention?
I thought light was momentum?

Doesn't the bending of spacetime by matter mean that light, which doesn't have any mass to interact with gravity, bends too? So there's no "centre of mass" for particles of light, but they don't follow straight lines, so space must be bent?

These are valid questions, do you have any answers?

Doesn't the bending of spacetime by matter mean that light, which doesn't have any mass to interact with gravity, bends too? So there's no "centre of mass" for particles of light, but they don't follow straight lines, so space must be bent?

I'm on my way to work, so I'll answer this question now.

It's not mass that warps space, it's energy density. This is what Einstein's equations say:

curvature = energy density.

Conversely, everything with energy (that means photons, too) interacts with space-time. So the fact that photons are massless doesn't mean that they aren't still stuck to space-time.

Right, right, right, but energy and mass are equivalent so a high energy density is the same as a large mass so lets not complicate the argument with semantics.

Right, right, right, but energy and mass are equivalent so a high energy density is the same as a large mass so lets not complicate the argument with semantics.

No.

The correct formula is

E^2 = m^2c^4 + p^2c^2

Photons have momentum, not mass.

Yes, I have a problem understanding momentum in this context. I know it as "mv" so when expressed as "p" I have difficulty visualising what it is. That is to say, how can things without mass have momentum.

For a photon,

p = \frac{2\pi\hbar}{\lambda}

where hbar is Planck's constant, and lambda is the wavelength.

Understood. Could you right down the equation representing the kinetic energy of a body with mass "m" travelling at velocity "v" using the full energy equation given earlier. Thus 1/2 mv^2 = what

Probably. For velocities much less than the speed of light, you can use

p = mv.

Fopr large velocities, youshould use the relativistic formula.

Understood. Could you right down the equation representing the kinetic energy of a body with mass "m" travelling at velocity "v" using the full energy equation given earlier. Thus 1/2 mv^2 = what

The total energy E' (rest energy + kinetic energy) of a massive body based on velocity is related to the body's rate of time dilation (Special Relativity):

E = m*c^2

E' = E / sqrt(1 - v^2/c^2) = sqrt(m^2*c^4 + p^2*c^2)

p = mv / sqrt(1 - v^2/c^2) .. This is the relativistic formula mentioned above by BenTheMan.

If v = 0 then p = 0, E' = E.

For the geometry-minded, it might help to remember that sqrt(1 - v^2/c^2) = cos(asin(v/c)).

Thanks shalayka...I couldn't remember where all the factors of v/c went, althought I SHOULD have been able to figure it out.

No probs. I also got inspired by your string theory thread and ordered a copy of A First Course in String Theory by Zweibach! Should be here next week sometime.

I'm looking forward to quasi-understanding what all you brane-iacs are talking about. :P

p = \frac{2\pi\hbar}{\lambda}Correct me if I am wrong, and I probably am, but isn't the Planck constant h, not hbar? Further, isn't \hbar = \frac{h}{2 \pi} by definition, which sort of rubbishes your equality? Just flying a kite here!

PS. Just looked in my yellowing undergraduate PhysChem text, where I re-discover this (from L. de Broglie).;

Assuming that the wave associated to an (electromagnetic) particle with energy E = h\nu (as I recall \nu is frequency), and E = m c^2, from Einstein, introduction of the equalities h \nu = m c^2 and \lambda = \frac{c}{\nu} and rearrangement yields \lambda = \frac{h}{mc}. And allowing p = mv and v = c (why?), then \lambda = \frac{h}{mv} = \frac{h}{p} = \frac{\hbar}{2 \pi p} . So p =\frac{2\pi\hbar}{\lambda} = \frac{h}{\lambda}.

Wow! What a surprise! Or have I missed some subtlety here?

Correct me if I am wrong, and I probably am, but isn't the Planck constant h, not hbar? Further, isn't \hbar = \frac{h}{2 \pi} by definition, which sort of rubbishes your equality? Just flying a kite here!

Nice catch.

If one multiplies \hbar (Dirac's constant) by 2\pi as he's doing, then the result is indeed just h (Planck's constant) as you mention. So I guess the formula ends up being correct in the end:

p = \frac{2\pi\hbar}{\lambda} = \frac{2\pi h}{2\pi\lambda} = \frac{h}{\lambda}.

Overlaps, you're quicker than me, man!

v = c (why?)

I think v = c because it's describing a limited case -- only photons. I could be misinterpreting his meaning though.

Ummm yes. I'm used to using hbar instead of h---it turns out to be more convenient in most interesting cases. Also, QuarkHead, I'd be careful dancing with equalities like

\lambda=\frac{h}{mc}

because m = 0 for photons. This is correct when dealing with, say, electrons. Also, E=mc^2 doesn't quite work for photons, either, because they have no mass. You need E = h\nu = pc etc. etc.

I also got inspired by your string theory thread and ordered a copy of A First Course in String Theory by Zweibach! Should be here next week sometime.

Here are some solutions to some of the exercizes:
http://www.pa.uky.edu/~jeremy/courses/strings/

Also, QuarkHead, I'd be careful dancing with equalities like

\lambda=\frac{h}{mc}

because m = 0 for photons. This is correct when dealing with, say, electrons.Yeah, that would be dancing with the devil, right enough. But you're right - I should have read the text, not just the math. They were talking about electrons, not photons (as one might expect from a chemistry text). Sorry.

Sorry.

If you'll forgive me for the S matrix fiasco (http://www.sciforums.com/showthread.php?t=76100), we'll call it even :)

Here are some solutions to some of the exercizes:
http://www.pa.uky.edu/~jeremy/courses/strings/

Excellent. Thank you!

They were talking about electrons, not photonsRight. Electrons will emit light (Bremsstrahlung) when their acceleration gets near c for a given medium. I think synchrotron radiation comes from this (accelerating electrons in a magnetic field) also. Has to do with interacting charge.

So electrons are photons, in a sense; or they give off energy by emitting light quanta.

That is the Cherenkov radiation. When the speed is more than the speed of light in the given medium, the object radiates light.

So electrons are photons, in a sense; or they give off energy by emitting light quanta.

Absolutely not. Electrons have spin 1/2, photons spin 1. Electrons are charged, photons are not.

And we have drifted off course again.

Absolutely not. Electrons have spin 1/2, photons spin 1. Electrons are charged, photons are not.

And we have drifted off course again.
Well, you're the captain, get the thing back on course.

These integral-spin photons, with zero charge, where do they come from, then?
Cerenkov radiation isn't the only name (or kind of emission), from relativistic electrons.

And we have drifted off course again.So let me try and drift us back on course, by paraphrasing a couple of Einsteins papers I have here. But, note, these both originate from well before he wrote down the field equations.

First he, E., that is, notes the equivalence principle: there is no objective way for an observer to distinguish gravity from acceleration.

Now, says he, consider two sets of rectangular coordinates {x,y,z} identical in all respects, and call these K and K'. Let their origins coincide. Imagine a circle drawn in the x,y plane of each. Now take a "standard measuring rod" and determine the ratio of circumference to diameter; in each case it will be \pi.

Now let K' rotate uniformly around the z-axis. Then, to an observer in K', the ratio above is still \pi. But due to the familiar length contraction of measuring rods in the direction of motion only, this ratio will appear to an observer in K is greater than \pi.

Thus, in a relativistic sense, Euclidean geometry fails for relatively accelerating systems (recal that any motion other than straight-line motion is an acceleration). In what way has Euclidean geometry broken down?

Consider, says E., the trajectory of a "particle" directed towards the origin of K', which appears, to an observer in K' to be a straight line, will appear to an observer in K to be curvilinear.

The equivalence principle then suggests, to E., that, due to gravity, spacetime is curved in a relativistic sense.

In a subsequent paper, Einstein goes on to show that any mathematical description of gravitation must be non-linear, in the sense that "gravitational energy", as he called it, is itself a gravitational source. This is the energy-density that Ben referred to; I will summarize this paper later.

My problem is understanding how curved space-time keeps objects on the ground back here on earth.

Read chapter 2 of this (no math, nice pictures):
fy.chalmers.se/~rico/Theses/tesx.pdf

Play around with this interactive diagram of curved spacetime:
adamtoons.de/physics/gravitation.swf
(add "www(dot)" in front, if needed)

I don't recall reading that.



I don't think the scale of a man is small enough to change the idea of warping space-time. In fact, the scale that the spacetime picture fails is much smaller than even an atom---it is the planck scale.

Apples and planets both move along geodesics in space-time. This is the basic idea. I should explain a few things here, and if you already know this, then I'll just waste the bandwidth.

If you've ever looked at the routes that airlines travel in the back of the magazine on an airplane, you'll notice that none of the lines are straight:

http://www.usairways.com/common/resources/_images/aboutus/pressroom/y_g_int_map.jpg

But you should have learned somewhere that the shortest (and quickest) distance between two points is a straight line. So are the air carriers of the world conspiring to make people late? No---they are travelling along the most efficient routes. On a curved surface, the shortest distance between two points is a great circle, and when projected onto a flat surface, the lines aren't straight anymore. On a geneal curved surface, these things are called geodesics.

Now, space-time is a curved surface. Matter and energy is bound to that surface, and quite generally we can argue that an object in freefall must travel along a geodesic. Why? Minimization of energy.

So the apple, when travelling in the earth's space-time, travels along a geodesic. That geodesic carries it towards the center of the earth. The planets exist in stable orbits about the sun's gravity well, and the moons about the planets.

This is explained very well indeed.

Einstein said that the quickest route from A to B was no longer a straight line, but it actually is. It's just that spacetime is almost flat, and that energy has a tension on spacetime itself, so it drags it's fabric with it. Energy itself fluxes into matter by curling into itself, or moving at fast enough speeds. Matter is then found to be nothing but a longer-lived fluctuation of a certain frequency.

If gravity is produced by curvature, and curvature is acceleration, then simply ''things'' move along such paths because it is caused by G_ab=T_ab, which describes the geometry of what it follows.

Energy itself fluxes into matter by curling into itself, or moving at fast enough speeds. I don't get this. Isn't energy the stuff that makes things move (in geodesics or whatever)?
How does energy curl into itself, exactly? Two bits of energy can "merge" and become bits of matter, is this what you're referring to?Electrons have spin 1/2, photons spin 1. Electrons are charged, photons are not.
Yes, this is basic quantum physics. So how do particles with no charge, interact with charged particles? Does spin come into it (is a photon-electron interaction anything to do with spin)? Are there any understandable explanations, for the mathematically challenged?

I don't get this. Isn't energy the stuff that makes things move (in geodesics or whatever)?
How does energy curl into itself, exactly? Two bits of energy can "merge" and become bits of matter, is this what you're referring to?Yes, this is basic quantum physics. So how do particles with no charge, interact with charged particles? Does spin come into it (is a photon-electron interaction anything to do with spin)? Are there any understandable explanations, for the mathematically challenged?

The equation of motions describe a thing moving through a spacetime map, and yes, does indeed require an energy to do so. But energy is a tension spacetime, in the sense that it curles into itself. If you cram-pack enough energy into a certain area so that there is no longer a sense of freedom, we have an infinite curvature and density. But bits of matter are ''fluxed'' energy, and as the theory goes right now, it is presented as being energy caught in knots...

... However, i have a more basic theory allowing energy to flux into matter via a frequency that would be like freezing it into a certain type of element, even though there is still inexorably movement. I'm only using the word ''freeze'' to help this analogy.

As for the question to Ben, can i just say that photons do not interact with each other because they fall into Bose-Einstein Condensate equations, and are then said to never interact with each other; but it is theoretically possible to use a mediator like an atom, and maybe clash two photons together, but the idea flies in the face of physics as we currently understand it.

For spin, well... it's not even properly understood. We aren't even sure what it is > apart from reverting to saying it has all spin directions (Up, Down and even a Sideways) spin simultaneously until a resolution or decoherence is made. As for the math of spin, it works out very well, but doesn't work out well at all for fermion particles.

photons do not interact with each other because they fall into Bose-Einstein Condensate equations, and are then said to never interact with each otherBut photons do interact with other photons. I know this because it's what happens in a lasing medium (all the photons are entrained to the same frequency and phase). What happens in a BEC, so that there isn't any photon-photon interaction?

Also, two high-energy photons can produce leptons, or fermions.
Photons are an interaction, fundamentally. They aren't separate, discrete things, until they "interact". There's this "time" stuff they disappear into, we only imagine that light, or any radiation, travels in straight lines.
I understand quantised spin as a quantised angular momentum, but because fundamental particles aren't like little billiards, it's hard to visualise a "spinning" wave-packet (for me, anyway).

''But photons do interact with other photons. I know this because it's what happens in a lasing medium (all the photons are entrained to the same frequency and phase). What happens in a BEC that means there isn't any photon-photon interaction?''

It means they tend to fall into the same states, and never interact... this is why they travel, like all bosons, in straight lines.

''Also, two high-energy photons can produce leptons, or fermions.
Photons are an interaction, fundamentally. They aren't separate, discrete things, until they "interact". There's this "time" stuff they disappear into, we only imagine that light, or any radiation, travels in straight lines.
I understand quantised spin as a quantised angular momentum, but because fundamental particles aren't like little billiards, it's hard to visualise a "spinning" wave-packet (for me, anyway).''

Right...

All Leptons and Fermions, and even the matter we do not see, all came from photons 32 years after spacetime expansion due to the laws of relativity. All matter in high energy collisions with their antipartners make this a high truth, since they revert back to photon energy... This means that all matter are just forms of ''trapped light''.

Photons mediate the electromagnetic force... they can interact with electrons because of this. You just have your idea's a bit muddled. They don't interact with each other also because of their neutral charge.

It means they tend to fall into the same states, and never interact... this is why they travel, like all bosons, in straight lines.How do they "fall into" the same state if there isn't any interaction between them? If they are waves of some kind, then they should interact. Why does the fact that they have no charge mean that there is no interaction?

And why do Bose-Einstein condensates not have any photon-photon interaction?

Bosons are force-carriers, but I'm not sure there is any way to determine that they "travel", or propagate, in nice straight lines. If they do, how do you explain double-slit interference patterns, produced by iteratively "firing" single photons through the slits on to a target?

''How do they "fall into" the same state if there isn't any interaction between them?''

They naturally fall into the same states, such as a speed, because of the following equations:

V =b/a=√(c2+(w/a)2)

The problem here, is that they are moving at a speed which exceeds ''c''. These are normal equations for any wave form or particle. The problem can be removed, by distinguishing this velocity which is known as the phase velocity vpr from another velocity known as the group velocity vgr which is given by,

vgr = c / vph

Now, this basically means that a wave packet will have a velocity at the value of ''c'' when in a group. If there is a single photon, uncertainty can take hold for a very short period and allow a photon to move faster than ''c''. It turns out that photons don't quite ''interact'' with each other in the sense one can hit off an electron, but there can diffraction and other wave phenomenon due to the wave equations. Therego, in a group, photons move together... The condensation of photons proved that they would do this, and allowed us to statistically determine the existence of the lazer.

Electrons however are not bosons, thergo do not follow Bose-Einstein Statistics but instead Fermi-Dirac Statistics... This means two electrons do interact with other. A prime example of this, is two electrons in an atom. When two of them come together, their spin states are determined. They exclude and cancel off each other all of the time... and is a major explanation to how we can have the elements we have on chart today.

''Bosons are force-carriers, but I'm not sure there is any way to determine that they "travel", or propagate, in nice straight lines. ''

They should travel in a straight line, so long as there is no gravitational disturbance.

''If they do, how do you explain double-slit interference patterns, produced by iteratively "firing" single photons through the slits on to a target?''

Photons will ''interfere'' with each other due to the wave function, but they do not interact with each other, as they would with electrons: Just remember this... waves interfere because they are not in particle form, when using the double slit experiment.

All Leptons and Fermions, and even the matter we do not see, all came from photons 32 years after spacetime expansion I think you will find that is 32 years, 4 months, 2 days, and 58 minutes, actually, to be precise.

I think you will find that is 32 years, 4 months, 2 days, and 58 minutes, actually, to be precise.

I do like accuracy.

Photons will ''interfere'' with each other due to the wave function, but they do not interact with each otherSorry, in my lab, photons "interfering" with each other are interacting.

Electrons interacting (like when two atoms get close to each other), do so by exchanging photons, or the electrons gain angular momentum, which is conserved by emitting a photon, or changing state (vibrational mode).

There seems to be a bit of misunderstanding of the term "interaction". What does "interact" mean, if photons don't do it (with, or to each other)? Momentum is what photons actually "are", specifically the momentum of a charged particle, despite not having any charge themselves, they are part of the "charged particle" scenario, and always have been. They aren't discrete, separate entities that arrive from nowhere in particular.

;)Having just joined the forum some of you will groan that I have brought this up again but I can't find the answer just by surfing around. So here goes with the question. I am almost prepared to accept that gravity is not a force as Newton thought but it is the result of warped space-time. Thus the earth creates a "well" in space because of and proportional to its mass. The moon orbits the earth trapped in the "well" but because of its speed it remains in orbit and doesn't crash down to earth. OK so far. Now my question doesn't refer to orbiting bodies but to earth bound objects. How does the warping of space explain why I don't just float off into space. Why did Newton's apple fall to eath. For me, a force is still involved. When the apple fell it accelerated at "g" because F=mg where F is the force of gravity not curved space. Any answers please?

We all know that gravity is one of the four fundamental forces of the universe: Electromagnetism, Strong and Weak Nuclear Force, Gravity. I think that space-time distortion and geometrical is a way to quantize gravity:D. :bugeye: Just as quantum field theory is used in place in the fundamental forces in supersymetry

Gravity is one of the fundamental forces: EW, GUT; Geometrical curvature is a schematic diagram of gravity as a force. This can be compared to quantum field theory. I think that the surface of earth and the collective mass of gases exhibits net gravitational waves that preclude an involuntary escape from this planet. God is a genius!!!!!!!;);)

Gravity is displayed through gravity by albert einstein as a warp in space-time. this a schematic diagram, not the excisement of this force.

Absolutely not. Electrons have spin 1/2, photons spin 1. Electrons are charged, photons are not.

what do scientists mean when they say that particles have spin? they're so small that it's impossible to observe an electron spin, so why do they say they have ½ or 1 spin?

Sorry, in my lab, photons "interfering" with each other are interacting.

Electrons interacting (like when two atoms get close to each other), do so by exchanging photons, or the electrons gain angular momentum, which is conserved by emitting a photon, or changing state (vibrational mode).

There seems to be a bit of misunderstanding of the term "interaction". What does "interact" mean, if photons don't do it (with, or to each other)? Momentum is what photons actually "are", specifically the momentum of a charged particle, despite not having any charge themselves, they are part of the "charged particle" scenario, and always have been. They aren't discrete, separate entities that arrive from nowhere in particular.


It seems as though i have been misunderstanding you.

When i talk about photon interference, i am meaning this in the sense that the wave's are incorporeal, and affect each other in statistical ways. You might even be lucky enough to decohere two photons due to the probability involved... a process of decoherence.

In the double-slit experiment, a few photons moving through one slit will be found to hit more of the screen than when counter-intuitively two slits are open. There waves of probability are striking each other as they pass the slits, and effect how many photons become particle-like..

If we are talking about ''rays'' of light... then photons follow straight lines... in accordance with Bose-Einstein statistics. It is, i am sure, theoretically assumable that if all matter is made up of photon energy, twice as much in magnitude, then there is an inverse law where one can smash two photons together to create a Lepton for instance...

what do scientists mean when they say that particles have spin? they're so small that it's impossible to observe an electron spin, so why do they say they have ½ or 1 spin?

We have observed spin though.

By the way, they are classed under as being an Integer 0, 1, 2, or half integer spins that is why, such as 1/2 and 3/2... If that answers your question. Half integer and integer spind make up the elements as we know it today.

why do they say they have ½ or 1 spin?Because they have angular momentum (spin, in ordinary language). It's quantised, so you get integral and fractional values (ratios of Planck's constant and pi). Quantum stuff is weird, but that's how spin is explained.

A photon can "additively" increase an electron's angular momentum (depending on its frequency), and an electron can conserve this by "subtracting" a photon (a quantised bit of energy) from itself. This is otherwise called "emission", or "propagation" of radiation. "They" can now reliably produce and detect single photons--their random nature has been tamed a bit.