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mauidon
2010-Nov-23, 04:53 PM
I am having a really hard time getting my head around gravity. If there was no mass in the universe would gravity still exist?
Is gravity only caused by mass bending spacetime?

In other words, where does gravity come from?

tommac
2010-Nov-23, 07:00 PM
Mass = Energy via E=MC^2

Either Mass or Energy ( really the same ) are the cause ( depending on how you look at it ) of gravity.

If there was no mass then there would be no gravity ... but I am not sure there would even be space.

I am having a really hard time getting my head around gravity. If there was no mass in the universe would gravity still exist?
Is gravity only caused by mass bending spacetime?

In other words, where does gravity come from?

caveman1917
2010-Nov-23, 10:19 PM
Mass = Energy via E=MC^2

Either Mass or Energy ( really the same ) are the cause ( depending on how you look at it ) of gravity.

If there was no mass then there would be no gravity ... but I am not sure there would even be space.

This is incorrect.

E² = (mc²)² + (pc)²

Mass indeed gives the biggest contribution to the energy content of our universe, and as such we easily approximate by saying that it is mass which 'produces' gravity. But really it is energy, and momentum will also give a (normally small) contribution. A photon for example will also induce a gravitational effect, even though it is massless, because it does have momentum.

ShinAce
2010-Nov-23, 10:46 PM
This is incorrect.

E² = (mc²)² + (pc)²

Mass indeed gives the biggest contribution to the energy content of our universe, and as such we easily approximate by saying that it is mass which 'produces' gravity. But really it is energy, and momentum will also give a (normally small) contribution. A photon for example will also induce a gravitational effect, even though it is massless, because it does have momentum.

Normally I would side with you that the full equation should be recognized. In this case, I feel it is unnecessary.

E=mc^2 means I can look at a basketball as having a certain mass, or containing a certain energy. Within the framework of gravity and relativity, either is fine.

Does everything we know of equate to energy, pretty much. Can we consider energy to cause spacetime curvature? Sure.

I applaud Tommac. This is the first time I've seen him answer a question.

caveman1917
2010-Nov-23, 11:05 PM
Normally I would side with you that the full equation should be recognized. In this case, I feel it is unnecessary.

I would tend to disagree, not so much about wether the full equation is recognized or not, but in that it shows something necessary for the OP question.
Namely it shows that the answer to

If there was no mass in the universe would gravity still exist?

is not

If there was no mass then there would be no gravity

but yes, as long as there is energy. A universe filled with only photons would have a non-flat curvature, even though there is no mass in that universe.

And i agree in applauding Tommac for answering the question, and his mistake is easily forgivable. But for correctness' sake it must be pointed out that his answer is incorrect.

ShinAce
2010-Nov-23, 11:17 PM
Tommac wrote:
"Mass = Energy via E=MC^2

Either Mass or Energy ( really the same ) are the cause ( depending on how you look at it ) of gravity."

Looks good to me. His next line I find even deeper than your interpretation. I choose to ignore 'If there was no mass then there would be no gravity' as explicit.

Without mass, how can we experience time? How do we define distance as observers are not exactly allowed?

At any rate, we're all giving the same answer. Mass and energy create spacetime curvature(or gravity).

edit: changed implicit for explicit....oops!

Strange
2010-Nov-23, 11:21 PM
And i agree in applauding Tommac for answering the question, and his mistake is easily forgivable. But for correctness' sake it must be pointed out that his answer is incorrect.

"Incomplete" might be a better characterization.

caveman1917
2010-Nov-23, 11:34 PM
Without mass, how can we experience time?

I'm not sure how to interpret that question. If there is no mass there is no "we", so we can't experience time.

How do we define distance as observers are not exactly allowed?

The same way we always do, by constructing a suitable metric.
The word "observer" strictly relates to an abstract frame of reference, which is certainly allowed in that case.
If you mean "observer" as a physically existing entity (ie with mass) then i'm again not sure how to interpret that question, since we excluded mass from that universe.

caveman1917
2010-Nov-23, 11:41 PM
"Incomplete" might be a better characterization.

You are right if one interprets the OP question as "what contributes to gravity?", in which case the answer "mass" would be incomplete.
But since the OP already seemed to be aware of the contribution by mass, i had interpreted the question as the binary "is mass the only contribution?", in which case there is one correct and one incorrect answer.

Not that i'm looking to argue this ad nauseam :)
Just wanted to point out the underlying reasoning for the word choice, it was certainly not intented as 'loaded' vs Tommac.

Jeff Root
2010-Nov-24, 01:15 AM
I would choose to understand Tom's statement as meaning that
energy implies mass: Without mass, there can be no energy.
If you could put enough light into a box to detectibly increase
the gravitational force exerted by the box, the inertial mass of
the box plus its contents would be exactly the mass required
to make it produce that increased gravitational force.

-- Jeff, in Minneapolis

astromark
2010-Nov-24, 01:49 AM
I am having a really hard time getting my head around gravity. If there was no mass in the universe would gravity still exist?
Is gravity only caused by mass bending spacetime?

In other words, where does gravity come from?

I bid you welcome... and draw your attention to...

......................... and then Tommac strided in with........................

Mass = Energy via E=MC^2

Either Mass or Energy ( really the same ) are the cause ( depending on how you look at it ) of gravity.

If there was no mass then there would be no gravity ... but I am not sure there would even be space. ... 'end quote.

............ @ Caveman1917.. you might actually be correct... but will by being too pedantic not answer the question asked...

Tommac has answered the question in a way that is easily understood...and left room for your point did he not ? Mark.

Cougar
2010-Nov-24, 02:18 AM
Yes, tommac almost had it, until he said:

If there was no mass then there would be no gravity ... but I am not sure there would even be space.

If there was no mass in the universe would gravity still exist?
Is gravity only caused by mass bending spacetime?

Wow, mauidon's first post! Welcome to the board!

I think everything caveman has said is correct, and ShinAce's point is well taken. I expect your concept or definition of "mass" is, well, straightforward? If you kick it, and it kicks back, that's mass? Suns and planets are massive bodies?

That's so 1700s. :razz:

So, yes, if the mass is in the form of energy, it still "bends spacetime." And, as caveman pointed out, momentum is also a component that affects the local bend of spacetime.

In fact, this question of "mass" has not been fully figured out, and is quite deep. For some decades we have known that "empty space" is, well, not empty. It seems the more we look, the less empty it is.

I notice the 2004 Nobel Prize winner in physics1 wrote:

What is space? An empty stage, where the physical world of matter acts out its drama? An equal participant, that both provides background and has a life of its own? Or the primary reality, of which matter is a secondary manifestation? Views on this question have evolved, and several times changed radically over the history of science. Today, the third view is triumphant.

After all, empty space is currently figured to contribute about 72.1% of the total gravitational spacetime curvature in the Universe.
____________________________________
1 Frank Wilczek, The Lightness of Being - Mass, Ether, and the Unification of Forces (2008).

RelativityWorks
2010-Nov-24, 02:33 AM
Well the stress energy tensor in einsteins field equation represents whatever is inside the curvature ( represented by the einstein tensor) both energy and mass.

caveman1917
2010-Nov-24, 02:51 AM
I would choose to understand Tom's statement as meaning that
energy implies mass: Without mass, there can be no energy.

But a photon has energy without mass.

If you could put enough light into a box to detectibly increase
the gravitational force exerted by the box, the inertial mass of
the box plus its contents would be exactly the mass required
to make it produce that increased gravitational force.

True, the mass of a system is that part of its energy that is Lorentz invariant (the same for all inertial observers). Which for a closed composite system such as you describe will also include the momenta of the subsystems (and the field energy of those).

But there is more to the story, a system of multiple photons does have a defined mass (this is used for constraints on the rest masses of the resulting particles in pair production). The mass is set as equal to the energy from the center of momentum frame for that system of photons. While this usage isn't lorentz invariant, it is physical (otherwise accelerator experiments wouldn't come out as predicted).
This would imply that a universe consisting of multiple photons does have mass, while one that consists of only a single photon doesn't :confused:

ETA: the above references to lorentz invariance don't seem to be getting to the real issue, mass is better seen as just the energy in the center of momentum frame

astromark
2010-Nov-24, 03:07 AM
Are you telling me that 'Empty' space has a gravity well.? Why do I suddenly want to argue this point ?

Please see that you are not helping. There's this newbie who asked where gravity comes from...

and Empty Space is not the answer is it.

Do not confuse the question 'mauidon' asked with a deeper discussion than is called for...

and I will assert that 'Tommac's' answer is correct in that without mass and energy driving the great expansion

and the effect we describe as gravity is in direct correlation to those things...

I find fault with a argument regarding empty space having gravity effect... That is not my understanding. Please explain?

caveman1917
2010-Nov-24, 03:31 AM
There's this newbie who asked where gravity comes from...

Ultimately gravity comes from the stress-energy tensor (http://en.wikipedia.org/wiki/Stress-energy_tensor). It is basically saying how energy and momentum is distributed and where it is going.

Cougar
2010-Nov-24, 03:35 AM
I find fault with a argument regarding empty space having gravity effect... That is not my understanding. Please explain?

Well, I guess there's a long explanation and a short one. I'll try the 2-word explanation: dark energy.

astromark
2010-Nov-24, 05:03 AM
That's very good... and perfectly acceptable. In a unacceptable way... I can live with that.

Infinitenight2093
2010-Nov-24, 07:49 AM
Ultimately gravity comes from the stress-energy tensor (http://en.wikipedia.org/wiki/Stress-energy_tensor). It is basically saying how energy and momentum is distributed and where it is going.

Is the stress-energy tensor where gravity comes from, or is it just describing where gravity might come from?...

tusenfem
2010-Nov-24, 09:29 AM
............ @ Caveman1917.. you might actually be correct... but will by being too pedantic not answer the question asked...

Next time you will receive an infraction.

CaptainToonces
2010-Nov-24, 09:47 AM
Well, I guess there's a long explanation and a short one. I'll try the 2-word explanation: dark energy.

But isn't dark energy a special form of energy that does not create a gravitational field like other mass/energy but rather EXPANDS the universe in an oppositional force to gravity? Or did you mean dark matter?

astromark
2010-Nov-24, 10:32 AM
We have labelled it 'Dark Energy' because we do not know a better name for it.
It being a unknown force that drives the eccelorating expansion.
While dark mater is the unseen but present mass found by the effect of gravity measured. Which could be energy as well.
I am not saying I can measure dark energy as a object of mass... it might be just energy.. That's the point of being 'Dark' we do not know.
Mater or energy ? I like the 'Stress-Energy Tensor.'

A point worth noting is surly that To answer the question in a manor and with intent to clarify and inform.
I do not think 'Mauidon' asked for a explanation of dark energies... and as to it having mass or gravity...
I saw a question wanting to explain a gravity well. That mass and energy and velocity all contribute to this answer...

Cougar
2010-Nov-24, 01:42 PM
But isn't dark energy a special form of energy that does not create a gravitational field like other mass/energy but rather EXPANDS the universe in an oppositional force to gravity? Or did you mean dark matter?

Dark energy accelerates the expansion, yes, but it also "weighs". It is responsible, in large part, for making the overall curvature of space flat - or Euclidian.

cosmocrazy
2010-Nov-24, 02:27 PM
So the basic layman's answer to the OP is,
Energy warps space-time and as the concentration of that energy increases so does the warping of space-time around it. So anything travelling along a path within the gravitational field of a given energy/matter source will naturally follow a curved path of the warped space. Matter being a very concentrated form of energy so the gravitational effects are much easier to measure, observe and experience. On to Black holes whose energy/matter density is so extreme that space-time is warped so much that even light cannot escape the curvature (gravity) of space-time..

tommac
2010-Nov-24, 02:34 PM
I thought the reason a photon provides a gravitational field is because of its energy? Or are you saying its energy is all momentum? But how can a massless particle have momentum?

This is incorrect.

E² = (mc²)² + (pc)²

Mass indeed gives the biggest contribution to the energy content of our universe, and as such we easily approximate by saying that it is mass which 'produces' gravity. But really it is energy, and momentum will also give a (normally small) contribution. A photon for example will also induce a gravitational effect, even though it is massless, because it does have momentum.

tommac
2010-Nov-24, 02:44 PM
Sorry ... the question was asked as newbie. I was going to go into zero point energy and that stuff but didnt want to confuse him as he was asking a question as a "noob".

I took his question to be that "is gravity and mass related?" more than "what other factors can affect gravity other than mass?"

The easy question and in my opinion is Mass for the beginner is gravity ... although energy can also produce gravity.

When you quoted me you left off an important part of my post before the quote you chose ... I posted:

Either Mass or Energy ( really the same ) are the cause ( depending on how you look at it ) of gravity.

Mixed with the quote below I was trying to imply that there is equivalent mass, without getting into too much detail.

So I will restate .. to say that if there is no mass ( or otherwise equivalent mass ) there would be no gravity.

Do you agree with that?

I would tend to disagree, not so much about wether the full equation is recognized or not, but in that it shows something necessary for the OP question.
Namely it shows that the answer to

is not

but yes, as long as there is energy. A universe filled with only photons would have a non-flat curvature, even though there is no mass in that universe.

And i agree in applauding Tommac for answering the question, and his mistake is easily forgivable. But for correctness' sake it must be pointed out that his answer is incorrect.

tommac
2010-Nov-24, 02:53 PM
Is the stress-energy tensor where gravity comes from, or is it just describing where gravity might come from?...

Isnt the stress energy tensor the sum of the gravity at each point?

Anyhow ... I doubt the original "noob" poster will find much use with the stress energy tensor to answer the question that he posed. If he wants to wrap his head around this ... introducing the stress energy tensor this early on is probably not a good idea.

tommac
2010-Nov-24, 02:54 PM
Are black holes mass or energy? ;-)

So the basic layman's answer to the OP is,
Energy warps space-time and as the concentration of that energy increases so does the warping of space-time around it. So anything travelling along a path within the gravitational field of a given energy/matter source will naturally follow a curved path of the warped space. Matter being a very concentrated form of energy so the gravitational effects are much easier to measure, observe and experience. On to Black holes whose energy/matter density is so extreme that space-time is warped so much that even light cannot escape the curvature (gravity) of space-time..

ShinAce
2010-Nov-24, 06:44 PM
Are black holes mass or energy? ;-)

Pick one, doesn't matter! Get it? It doesn't matter!

Moving along. I used to like to think that matter was converted to massless particles at the singularity. Truth is, until we have a quantum theory of gravity, your question will remain unanswered.

tommac
2010-Nov-24, 07:01 PM
The questions was somewhat rhetorical as an attempt to illustrate the nitpick.

Pick one, doesn't matter! Get it? It doesn't matter!

Moving along. I used to like to think that matter was converted to massless particles at the singularity. Truth is, until we have a quantum theory of gravity, your question will remain unanswered.

ShinAce
2010-Nov-24, 07:10 PM
And it went right by me! Dear me...

Ken G
2010-Nov-24, 07:22 PM
In other words, where does gravity come from?
Although many good answers have been given already about the nature of energy and gravity, I suspect the actual answer to your question is "no one knows." Indeed, I think your confusion stems not from failing to understand gravity, it stems from asking for more from an understanding of gravity than such an understanding is capable of providing. It is the nature of science to make models, but we never get to know why those models work, until we find a deeper model that includes it-- only to be presented with the same question about the deeper model. You are not supposed to know where gravity comes from, no one knows that-- all we know is that we can successfully model the effects of gravity by saying that it is a curvature of spacetime due to the presence of stress-energy, which usually amounts to the presence of rest mass and some kind of mysterious vacuum energy.

Zach Singer
2010-Nov-24, 07:41 PM
Excuse me for being another newb but: In regards to groups of photons having mass and individual photons not (and correct me if i interpreted that portion of the discussion wrong) if a photon did not have momentum would it still be a photon? Would it assume mass and behave differently? And if so, if the photon does have momentum but is the observers frame of reference instead of that which is being measured does the rest of the universe (or a specific part of it like a star or planet that would otherwise form the frame of reference) behave mathematically like light?

Cougar
2010-Nov-24, 08:26 PM
That's very good... and perfectly acceptable. In a unacceptable way...

:lol:

Ken G
2010-Nov-24, 11:12 PM
Excuse me for being another newb but: In regards to groups of photons having mass and individual photons not (and correct me if i interpreted that portion of the discussion wrong) if a photon did not have momentum would it still be a photon?The issue of whether or not photons have mass has to do with which interpretation of "mass" is used, not how many there are. Mass usually means "rest mass", which photons have none of, but it can also mean "relativistic mass", which is really just another way to say E/c2, where E is their energy-- which photons do have. If a photon had no momentum, it would also have no energy, and would not exist at all.

Would it assume mass and behave differently?Photons have momentum by virtue of having energy, not by virtue of having rest mass. But even a massless particle has energy E and momentum p, where p = E/c. The E can be anything, but will associate with a frequency of E/h, where h is a very tiny constant called Planck's constant.

And if so, if the photon does have momentum but is the observers frame of reference instead of that which is being measured does the rest of the universe (or a specific part of it like a star or planet that would otherwise form the frame of reference) behave mathematically like light?Yes, if you could enter the photon's frame, everything else in the universe would move at c, so would be a lot like light. You can't actually enter the photon frame because a frame moving at c has singular mathematical properties, but you can take the limit of what you see as you get closer and closer to c, and everything else will look like it's coming at you at near c. That means everything else will appear to have a huge energy, much more than its own rest mass-energy, and that means it will all be behaving a lot like very very high-frequency light.

caveman1917
2010-Nov-25, 09:16 AM
Is the stress-energy tensor where gravity comes from, or is it just describing where gravity might come from?...

Science doesn't differentiate between those two. All we have is models, and in our current model (GR) the stress-energy tensor is the 'source' of the Einstein tensor. The einstein tensor tells us the curvature of spacetime, while the stress-energy tensor tells us the distribution of energy and momentum. So by that model the curvature (ie gravity) is 'produced' by the distribution of energy.

caveman1917
2010-Nov-25, 09:32 AM
I thought the reason a photon provides a gravitational field is because of its energy? Or are you saying its energy is all momentum? But how can a massless particle have momentum?

The energy is indeed all momentum. If you look at the equation given, and set m=0 (photon has no mass), you see that it reduces to E=pc (p is momentum), the energy comes solely from the momentum. As to how a massless particle can have momentum, think of it the other way. How could a massless particle not have momentum? If we set both m=0 and p=0 in that equation, the energy (E) also becomes 0, and we have nothing left, there is no particle then. A massless particle must have momentum to exist.

I'm not sure how familiar you are with SR, but it also gives a (perhaps more intuitive) way of arriving at that conclusion. You have heard it said that it is 'illegal' to take the reference frame of a particle moving at c? Since the way in which we can reduce momentum to 0 is by taking the reference frame of that particle (so it is at rest in that frame), and the previous fact that there are no valid rest frames for massless particles, this means there is no way to set its momentum to 0, it must always have a momentum.

caveman1917
2010-Nov-25, 09:45 AM
Sorry ... the question was asked as newbie. I was going to go into zero point energy and that stuff but didnt want to confuse him as he was asking a question as a "noob".

I took his question to be that "is gravity and mass related?" more than "what other factors can affect gravity other than mass?"

The easy question and in my opinion is Mass for the beginner is gravity ... although energy can also produce gravity.

When you quoted me you left off an important part of my post before the quote you chose ... I posted:

Mixed with the quote below I was trying to imply that there is equivalent mass, without getting into too much detail.

So I will restate .. to say that if there is no mass ( or otherwise equivalent mass ) there would be no gravity.

Do you agree with that?

As KenG noted there is an important distinction between relativistic mass and invariant mass (or "rest mass"). If the term "mass" is given without specification it is assumed to relate to invariant mass, and as such i have been responding to your posts. If you specifically meant relativistic mass i would agree that any energy can be expressed in such a relativistic mass perspective. Though the entire concept of relativistic mass has fallen out of flavour (mass should not be an observer dependent quantity), and it is preferred to use energy to talk about the entire energy, and use mass only for the invariant part.

caveman1917
2010-Nov-25, 09:59 AM
Excuse me for being another newb but: In regards to groups of photons having mass and individual photons not (and correct me if i interpreted that portion of the discussion wrong) if a photon did not have momentum would it still be a photon? Would it assume mass and behave differently? And if so, if the photon does have momentum but is the observers frame of reference instead of that which is being measured does the rest of the universe (or a specific part of it like a star or planet that would otherwise form the frame of reference) behave mathematically like light?

The issue of whether or not photons have mass has to do with which interpretation of "mass" is used, not how many there are.

This is also what i thought, but apparently a non-zero invariant mass is defined for a system of many photons. In general there will exist a unique frame in which the added momenta of the photons is minimized, the energy of the system in this frame is taken to be the invariant mass of that system.

It appears this is needed in pair production, where this mass gives the upper bound to the combined rest masses of the resulting particles, and in that sense the quantity seems to be physically relevant, not just sheer convention. It is in this way that invariant mass becomes a conserved quantity. If i have understood this all correctly.

This use of invariant mass seems a bit esoteric to me but who am i to judge of course :)

cosmocrazy
2010-Nov-25, 05:18 PM
Are black holes mass or energy? ;-)

You tell me..

Does anybody really know what black holes are, or at least what becomes of the matter and energy sucked in?

All we know is that they are regions in space-time where the escape velocity exceeds light speed, oh... and we can theorise on the other details.

tommac
2010-Nov-25, 09:47 PM
well what are they per GRs definition ... mass OR energy?

You tell me..

Does anybody really know what black holes are, or at least what becomes of the matter and energy sucked in?

All we know is that they are regions in space-time where the escape velocity exceeds light speed, oh... and we can theorise on the other details.

ShinAce
2010-Nov-25, 10:05 PM
well what are they per GRs definition ... mass OR energy?

I'd say as per GR, they are solutions!

tommac
2010-Nov-25, 10:07 PM
I'd say as per GR, they are solutions!

So solutions create gravity? Can you explain ?

WayneFrancis
2010-Nov-25, 10:43 PM
well what are they per GRs definition ... mass OR energy?

This is for the lurkers since tommac ignores all my posts. GR doesn't say if they are mass or energy. GR doesn't care one way or another since to GR they can be equivalent. It is like asking some that just got a surprise birthday party thrown for them if their cake was baked in a gas or electric oven. To the birthday person, who doesn't know anything about where the cake was made, it doesn't matter if it was cooked in an electric or gas oven. The end result is the same.

WayneFrancis
2010-Nov-25, 10:46 PM
So solutions create gravity? Can you explain ?

Again for the lurkers another analogy is like saying

2 * 4
and
3 + 5
are both valid solutions to the question "can you provide an equation that = 8"

maths is agnostic to the question of which one is better just as GR is agnostic to the question of "Are black holes mass or energy?"

Strange
2010-Nov-25, 10:58 PM
well what are they per GRs definition ... mass OR energy?

Well, as you said back in post #2, mass and energy are equivalent so it doesn't make any difference. Especially as we can never "see" what goes on inside the event horizon. It may be mass or energy or a mixture or something else that we don't yet understand.

tommac
2010-Nov-25, 11:11 PM
I am in full agreement!

Well, as you said back in post #2, mass and energy are equivalent so it doesn't make any difference. Especially as we can never "see" what goes on inside the event horizon. It may be mass or energy or a mixture or something else that we don't yet understand.

cosmocrazy
2010-Nov-26, 06:08 PM
I am in full agreement!

So what was the nitpick?

I'd stated in my original post in layman's terms - energy/matter - meaning energy or matter or a combination of both. I don't see the point of going into a debate of what really is going on inside a BH, since nobody knows for sure. All we do know is it appears that energy and matter or a combination of both warps space-time. And that a black hole is the most extreme example of that warping that we know of.

tommac
2010-Nov-27, 08:49 PM
This was:

This is incorrect.

E² = (mc²)² + (pc)²

Mass indeed gives the biggest contribution to the energy content of our universe, and as such we easily approximate by saying that it is mass which 'produces' gravity. But really it is energy, and momentum will also give a (normally small) contribution. A photon for example will also induce a gravitational effect, even though it is massless, because it does have momentum.

So what was the nitpick?

I'd stated in my original post in layman's terms - energy/matter - meaning energy or matter or a combination of both. I don't see the point of going into a debate of what really is going on inside a BH, since nobody knows for sure. All we do know is it appears that energy and matter or a combination of both warps space-time. And that a black hole is the most extreme example of that warping that we know of.

caveman1917
2010-Nov-27, 09:40 PM
This was:

No, it wasn't. The question about the form of the energy within the event horizon of a black hole is a different question than wether mass is the only contribution to gravity.

Atlas shrugged
2010-Nov-27, 09:57 PM
Take a bed sheet and have two people hold it open real tight, now place a basketball in the center.The well created by the ball is the same thing gravity looks like in the fabric of spacetime.

The sheet represents spacetime and the ball is the mass creating Gravity just as the Sun does and any tiny balls which have momentum are forced to circle it, just like the planets do around the Sun.

tommac
2010-Nov-28, 02:24 AM
You asked what was the nit pick ... that was the nit pick that I was referring to.

This is incorrect.

E² = (mc²)² + (pc)²

Mass indeed gives the biggest contribution to the energy content of our universe, and as such we easily approximate by saying that it is mass which 'produces' gravity. But really it is energy, and momentum will also give a (normally small) contribution. A photon for example will also induce a gravitational effect, even though it is massless, because it does have momentum.

No, it wasn't. The question about the form of the energy within the event horizon of a black hole is a different question than wether mass is the only contribution to gravity.

caveman1917
2010-Nov-28, 12:51 PM
Take a bed sheet and have two people hold it open real tight, now place a basketball in the center.The well created by the ball is the same thing gravity looks like in the fabric of spacetime.

The sheet represents spacetime and the ball is the mass creating Gravity just as the Sun does and any tiny balls which have momentum are forced to circle it, just like the planets do around the Sun.

A somewhat better analogy might be to place a basketball on a bed, and then start pulling the bedsheet towards you (you are the gravitating body in this way of looking at it), the basketball being dragged along with the 'falling' space is what we then think of as gravity.

cosmocrazy
2010-Nov-29, 05:57 PM
You asked what was the nit pick ... that was the nit pick that I was referring to.

Yes and in my original post I clearly stated "Matter being a very concentrated form of energy", which was intended as a simple layman's answer to the OP.

tommac
2010-Nov-29, 06:40 PM
Yes and in my original post I clearly stated "Matter being a very concentrated form of energy", which was intended as a simple layman's answer to the OP.

Agreed!

cjameshuff
2010-Nov-29, 06:50 PM
A somewhat better analogy might be to place a basketball on a bed, and then start pulling the bedsheet towards you (you are the gravitating body in this way of looking at it), the basketball being dragged along with the 'falling' space is what we then think of as gravity.

Not much better, it gives the impression space-time is being "sucked into" mass.

Gravity in GR is purely geometric. Consider two wheels fixed to an axle so they can't roll independently...what happens if one is smaller than the other, and you roll them across a flat surface? The pair follows a circular path, because one wheel covers less distance than the other. If the wheels are the same size, they roll in a straight line. If they are the same size, but the surface they're rolling on is curved like the usual "rubber sheet model", the set of wheels rolls in a straight line across the surface, which is a curved line when viewed from above. The wheel toward the depression would have to travel a longer distance for the pair to travel a straight line as viewed from above, instead, the set turns toward the region of higher curvature. More, it does so whether it's going past a depression or a hill. It's not rolling downhill on a sheet or being pulled in along with the sheet beneath it, it's just going in what it considers a straight line.

caveman1917
2010-Nov-29, 09:52 PM
Not much better, it gives the impression space-time is being "sucked into" mass.

I was under the impression that to picture space as being "sucked into" mass was a pretty good analogy for the actual math, as far as analogies go.

Gravity in GR is purely geometric. Consider two wheels fixed to an axle so they can't roll independently...what happens if one is smaller than the other, and you roll them across a flat surface? The pair follows a circular path, because one wheel covers less distance than the other. If the wheels are the same size, they roll in a straight line. If they are the same size, but the surface they're rolling on is curved like the usual "rubber sheet model", the set of wheels rolls in a straight line across the surface, which is a curved line when viewed from above. The wheel toward the depression would have to travel a longer distance for the pair to travel a straight line as viewed from above, instead, the set turns toward the region of higher curvature. More, it does so whether it's going past a depression or a hill. It's not rolling downhill on a sheet or being pulled in along with the sheet beneath it, it's just going in what it considers a straight line.

Suppose you have your standard test particle, and in a very newtonian way you imagine applying a force, not on the particle itself but on the theoretical little "box" of space around it (ie you're "sucking in" the space), this will also easily visualise why inertial paths are curved the way they do (and in the same simple picture get you Shapiro delay, event horizons and some other GR "quirks" such as frame dragging).

But the main advantage i believe this analogy to have is that you can get orbits for particles starting at rest immediately, whilst for the rubber sheet analogy you have to invoke some extra 'downwards' gravitational force (the thing that makes stuff start rolling down the gradient in the first place). Though your analogy may be closer to everyday experience - we 'know' stuff rolls 'down' an unever rubber sheet - i think there might be more merit in the 'falling space' picture which seems completer and more accurate.

Jeff Root
2010-Nov-29, 11:18 PM
It is ironic that the rubber sheet analogy uses gravity to
explain gravity. But it seems to be a pretty good analogy.

It may have been here on BAUT that I first learned that the
space around a black hole can be considered to be "moving"
or "flowing" into the black hole. Although I first thought it only
applied inside the last stable orbit, I don't see how it could not
apply to any gravity source. But it sounds uncomfortably like
an assertion that space has material substance, which I know
it does not.

-- Jeff, in Minneapolis

caveman1917
2010-Nov-29, 11:38 PM
But it sounds uncomfortably like
an assertion that space has material substance, which I know
it does not.

So does the rubber sheet ;)

If you can stretch it, you can eat it :)

cjameshuff
2010-Nov-30, 12:23 AM
I was under the impression that to picture space as being "sucked into" mass was a pretty good analogy for the actual math, as far as analogies go.

I've mostly heard such things from people trying to push some variant of aether theory.

But the main advantage i believe this analogy to have is that you can get orbits for particles starting at rest immediately, whilst for the rubber sheet analogy you have to invoke some extra 'downwards' gravitational force (the thing that makes stuff start rolling down the gradient in the first place). Though your analogy may be closer to everyday experience - we 'know' stuff rolls 'down' an unever rubber sheet - i think there might be more merit in the 'falling space' picture which seems completer and more accurate.

It is ironic that the rubber sheet analogy uses gravity to
explain gravity. But it seems to be a pretty good analogy.

I specifically stated there was no such downward force. It does not use gravity to explain gravity. I repeat, it's not rolling downhill. The explanation is purely geometric. Again, it works just as well for a hill as it does for a depression. Trajectories don't go "downhill", they bend in the direction of greater curvature as they follow a straight line across the surface. The greater curvature is toward the masses causing the curvature.

The rubber sheet model is an illustration of how curved space can cause effects that seem like gravity. Neither that "aether-drain" model nor the common but incorrect "rolling downhill" rubber sheet model do so. It's all about curvature and the geometry of the surface of the sheet, not about rolling downhill on a slope.

Jeff Root
2010-Nov-30, 01:28 AM
Every rubber sheet analogy I've seen or have introduced myself used
gravity to explain gravity. You might have one that doesn't, but if you
explained it in the last few posts, I've already forgotten it.

-- Jeff, in Minneapolis

cjameshuff
2010-Nov-30, 01:42 AM
Every rubber sheet analogy I've seen or used myself used
gravity to explain gravity. You might have one that doesn't,
but if you explained it in the last few posts, I've already
forgotten it.

It's intended as an illustration of how curved spacetime causes gravity...objects following geodesics through curved spacetime. It doesn't make any sense to just consider objects to be rolling down the sheet in a gravity field...that completely fails to show how gravity has anything to do with the curvature of spacetime. You're using the same broken, misunderstood version that the critics of the rubber sheet model do when they say it doesn't explain anything. By ignoring (forgotten? Sure...) the explanation that actually explains something and sticking with the broken, meaningless non-explanation, you're just intentionally spreading misinformation and doing nothing of help to anyone.

tommac
2010-Nov-30, 01:43 AM
I actually think the rubber sheet analogy is pretty good when it comes to analogies. You have to really push the analogy for it to fall apart.

Jeff Root
2010-Nov-30, 02:03 AM
While I think the rubber sheet analogy is pretty good, I think it can
fail spectacularly and *very* easily. However, I don't understand
why CJH says I'm intentionally spreading misinformation when I
use it, or what he's suggesting as an alternative. If there were a
good alternative, we'd all be using it.

Also, I'm not sure whether I've ever said anything about objects
"rolling" on the rubber sheet. I would think that I've probably tried
to avoid using the term "roll" since rolling is (obviously) irrelevant.

-- Jeff, in Minneapolis

WayneFrancis
2010-Nov-30, 03:30 AM
Every rubber sheet analogy I've seen or have introduced myself used
gravity to explain gravity. You might have one that doesn't, but if you
explained it in the last few posts, I've already forgotten it.

-- Jeff, in Minneapolis

But from the explanation about the 2 identically sized wheels rolling on a curved slope does explain it well.

But lets go with another analogy. The ant walking a straight line on the rubber sheet. The ant isn't "falling" into the depression when it, from above, follows a curved path. It is just walking a straight line. No gravity in that scenario to explain space curvature...besides keeping the ant on the sheet to begin with...but if you did the experiment in zero g the ant would still follow the curved path.

Jeff Root
2010-Nov-30, 05:43 AM
Rolling balls take elliptical paths around an appropriately-shaped
depression. Axle-connected wheels do not.

-- Jeff, in Minneapolis

Ken G
2010-Nov-30, 06:13 AM
But lets go with another analogy. The ant walking a straight line on the rubber sheet.
All of these analogies suffer from some pretty bad weaknesses. On balance, I don't like them-- they are really more for creating the illusion of understanding, rather than the genuine article. If one uses gravity to explain gravity, then of course the curved surface is doing nothing more than canceling a component of gravity and leaving another one to cause the curved motion, so it's not really an effect of curvature, it's a gravitational effect. The ant walking a straight line has its own problems-- it suggests that all ants, no matter what speed they walk, would follow that same path, which doesn't explain how orbits work. (The straight line on a curved surface does work, but only a curved surface in spacetime, not a curved purely spatial surface. So I'm all right with it if we say the ant is walking a line in spacetime, but curved surfaces in spacetime are still pretty difficult to get your head around.)

I prefer to chuck the whole issue of curvature, even though it is geometrically correct, and just use the equivalence principle. The equivalence principle says that what we perceive as gravity is actually a failure to correctly identify the inertial paths. The inertial paths are the paths of free-fallers and orbiters of all kinds, and anything else is on an accelerated path, like us in our chairs. You can imagine that "space itself" is falling, that gravity is essentially the falling of space, so we need to accelerate opposite to the falling space just to maintain a fixed distance from people on the opposite side of Earth. This doesn't do justice to the more bizarre aspects of spacetime curvature, like tidal effects, but it gets the basic trajectory of a particle right, by the equivalence principle.

Strange
2010-Nov-30, 11:12 AM
I've mostly heard such things from people trying to push some variant of aether theory.

I first heard this analogy from Ken G (although now he says he doesn't like any of them :)) probably in relation to how light cannot escape a black hole It worked pretty well in that context (given the level of the question and explanations). I think it is quite a useful addition to the "arsenal of analogies". The most important thing (that is so often omitted) is to make it clear to the reader that they are just [limited] analogies.

caveman1917
2010-Nov-30, 12:09 PM
I specifically stated there was no such downward force. It does not use gravity to explain gravity. I repeat, it's not rolling downhill. The explanation is purely geometric. Again, it works just as well for a hill as it does for a depression. Trajectories don't go "downhill", they bend in the direction of greater curvature as they follow a straight line across the surface. The greater curvature is toward the masses causing the curvature.

But if all your analogy does is show how a straight line can come out as curved on a curved surface, how is it any more useful than just pointing to a map of earth with airliner-paths plotted on it?

The rubber sheet model is an illustration of how curved space can cause effects that seem like gravity. Neither that "aether-drain" model nor the common but incorrect "rolling downhill" rubber sheet model do so. It's all about curvature and the geometry of the surface of the sheet, not about rolling downhill on a slope.

Sure they both do, the "falling space" one i have explained a couple of posts earlier how locally straight lines come out as globally curved. The rubber sheet also does, but requires an extra gravitational force.

ETA: And you'll have to be clear that one dimension of your curved rubber sheet is a temporal one, the path connects events in spacetime (it is the curvature of spacetime, not space as you claim).

caveman1917
2010-Nov-30, 12:15 PM
I first heard this analogy from Ken G (although now he says he doesn't like any of them :)) probably in relation to how light cannot escape a black hole It worked pretty well in that context (given the level of the question and explanations).

I think it was in relation to that youtube video where some professor was explaining what happened when you fall into a black hole, IIRC.

I think it is quite a useful addition to the "arsenal of analogies". The most important thing (that is so often omitted) is to make it clear to the reader that they are just [limited] analogies.

I agree fully, analogies are never a substitute for the actual math. But i believe that doesn't mean all analogies are equal, there is relative merit to them, and i think it is for those not able/willing to spend years learning GR important that the analogy be chosen carefully that can be pushed as far as possible, and intuitively incorporate as many effects as possible without breaking.

cjameshuff
2010-Nov-30, 01:48 PM
But if all your analogy does is show how a straight line can come out as curved on a curved surface, how is it any more useful than just pointing to a map of earth with airliner-paths plotted on it?

How does that illustrate anything that bears more than the slightest resemblance to gravity?

Sure they both do, the "falling space" one i have explained a couple of posts earlier how locally straight lines come out as globally curved. The rubber sheet also does, but requires an extra gravitational force.

That's absurd. Why bother with the rubber sheet, a simple inclined plane "explains gravity" just as well...that is, it explains nothing.

ETA: And you'll have to be clear that one dimension of your curved rubber sheet is a temporal one, the path connects events in spacetime (it is the curvature of spacetime, not space as you claim).

Funny you you pick the one instance where I omitted "time" out of all my posts in this thread.
Quit arguing to win the argument, and listen to what I'm saying.

The ant walking a straight line has its own problems-- it suggests that all ants, no matter what speed they walk, would follow that same path, which doesn't explain how orbits work. (The straight line on a curved surface does work, but only a curved surface in spacetime, not a curved purely spatial surface. So I'm all right with it if we say the ant is walking a line in spacetime, but curved surfaces in spacetime are still pretty difficult to get your head around.)

This is why I'm careful to emphasize that it's curved spacetime (thoughI do occasionally slip, like the instance caveman1917 jumped on). Curved space alone is sufficient to show how a curved trajectory results, though, and the analogy's typically offered as an explanation for how a straight geodesic can appear to be a curved trajectory.

I prefer to chuck the whole issue of curvature, even though it is geometrically correct, and just use the equivalence principle. The equivalence principle says that what we perceive as gravity is actually a failure to correctly identify the inertial paths.

That might be more useful from an analytical standpoint, but I doubt the target audience of the rubber sheet analogy will benefit from it.

caveman1917
2010-Nov-30, 03:55 PM
How does that illustrate anything that bears more than the slightest resemblance to gravity?

It doesn't, but that was my point. Neither does your analogy, other than show how inertial paths appear curved globally. And i am very well aware what you are saying is pretty much a strict exposition of the underlying phenomenom. What i am arguing with is how useful that analogy is for providing a mental framework in which to understand how things play out, which is after all the entire point of analogies. How many aspects can someone using that analogy clear up for himself? That, for me, is the basis for which to compare the relative merit of analogies.

That's absurd. Why bother with the rubber sheet, a simple inclined plane "explains gravity" just as well...that is, it explains nothing.

It's not absurd, roll a ball in a straight line over some fabric, pull the fabric, and the resulting path comes out curved.
And nobody should bother with the rubber sheet, it is highly flawed in design.

Funny you you pick the one instance where I omitted "time" out of all my posts in this thread.

Within your analogy, imagine putting a test particle at rest wrt the primary. Explain the resulting trajectory.
You can't do this without making it clear the curvature relates to spacetime, not space. Good luck having anyone without the necessary background wrap their head around that one.
That was the point i was trying to make by jumping on that remark, you're merely trying to make the analogy as close as possible to the actual phenomenon without regards as to actually making it more intuitive.

Quit arguing to win the argument, and listen to what I'm saying.

I do listen to what you are saying, and yes the phenomenom is geometric in origin and your exposition is strictly correct, nobody (at least not me) is arguing that.
What i'm saying is that what you have may be a good remark to go with an actual textbook on GR, but it has no use as an analogy (ie for those who will not bother with GR anyway).

Suppose you gave someone that analogy, and afterwards they ask themselves how an event horizon works? How it is that light gets delayed coming from deeper in a gravitational field? And numerous other things. How many of those will they be able to intuitively figure out for themselves using your analogy? None. That is my argument, your analogy has no use unless someone is already determined to study GR, in which case one doesn't need analogies in the first place.

Perhaps we look for different things when comparing the merits of analogies, in which case i suppose we'll have to just agree to disagree. But i feel that doesn't necessitate accusations of just arguing to win an argument nor of not listening to the counterarguments being made.

Jeff Root
2010-Nov-30, 06:11 PM
I first heard this analogy from Ken G (although now he says
he doesn't like any of them :)) probably in relation to how
light cannot escape a black hole
I think the analogy you're talking about is that of stretching space
around a black hole, so that it is as if the space were flowing into
the black hole. Right? I couldn't remember whether it was Ken or
Richard or possibly DrRocket or someone else who introduced the
idea, and the others did not object strenuously. I can't remember
whether Kip Thorne uses it in 'Black Holes & Time Warps'.

The basic rubber sheet analogy has been used far more widely.
The shape of the sheet is a graph of gravitational potential. The
paths of objects sliding or rolling across the surface very closely
mimic the paths of objects in gravity. You can get straight-line,
hyperbolic, parabolic, elliptical, and circular trajectories. It very
clearly illustrates Wheeler's great characterization that "Matter
tells space how to curve; space tells matter how to move."

It is usually not pointed out that the curvature is in the time
direction. Some people apparently get the incorrect impression
that the curvature is in three-dimensional space. More, I think,
including me, get the incorrect impression that the curvature is
in a fourth spatial dimension. But space curving in the direction
of time is an awfully difficult concept, especially when, as is
usually the case, the exposure to these ideas is only a single
article in a magazine, a single chapter in a book, or a single
hour-long TV program. That's as long as an author can plan to
hold onto his audience in most cases.

Even Wheeler said "space" in the quote above, not "spacetime".

-- Jeff, in Minneapolis

Jeff Root
2010-Nov-30, 06:21 PM
I just said that the shape of the rubber sheet is a graph of
gravitational potential. But I'm confused now whether it is
in fact potential or gravitational field strength. What's the
difference?

-- Jeff, in Minneapolis

Ken G
2010-Nov-30, 07:07 PM
That might be more useful from an analytical standpoint, but I doubt the target audience of the rubber sheet analogy will benefit from it.Surprisingly, I don't find that is always true. Sometimes what people find hard to understand is not at all what we might expect. For example, some people have a hard time doing any kind of mathematical calculation themselves, but if you tell them that the curved trajectory (in space and time) of a baseball is (close to) the force-free path any object at that speed would take in the presence of that gravity, they are fine with it. Especially if no one has ever told them Galileo's mistake that force-free paths are straight lines! We just don't tell them Newton's first law, and instead start from a different set of inertial behaviors, and then tell them how real forces cause deviations from those inertial paths, and they might be just fine. After all, the ancient Greeks were fine with the idea that an unforced (or most natural) trajectory is one where the object slows to a halt, so we cannot say that Galileo's version is naturally intuitive. Ironically, the ancient Greeks also thought that an unforced (or most natural) path is one where the object falls to the ground, and they were actually closer to right on that one than Galileo was (at least in GR, anyway).

Ken G
2010-Nov-30, 07:11 PM
But I'm confused now whether it is
in fact potential or gravitational field strength. What's the
difference?A potential is a scalar field (so a number at every point), but the gravitational field is a vector (an arrow at every point), given by the gradient of the scalar field. So one leads to the other, they are closely connected.