How does gravity curve spacetime?

[Naty1]

How does the self interaction of gravity (gravitons) shape spacetime? What's the quantum mechanism? Or a wave description?

(In a related thread I asked "How does the speed of light vary in the presence of a magnetic field. We concluded it did not, but that it does curve. Photons always move at "c". So here I am inquiring why space curves as that is what causes light to curve.)

From Lee Smolin's book, THE TROUBLE WITH PHYSICS, page 85:

...gravitational waves interact with anything that has energy and (so) they interact with each other. This problem does not occur with electromagnetic waves...because photons do not interact with each other...describing the self interaction of gravitons consistently turned out to be a tough nut to crack...the failure to solve this problem is a consequence of not taking Einstein's principle of background independence seriously. Once the gravitational waves interact with one another, they can no longer been seen as moving on a fixed background (of spacetime)...They change the background as they travel...by now almost everyone who thinks seriously about quantum gravity agrees...

So the answer apparently lies within a background independent quantum gravity formulation...perhaps loop quantum gravity. It MAY also be this question: How does a passing gravitational wave (or gravitons) change a Penrose spin network construct of spacetime? (Think of a geodesic dome, with integer value nodes for areas and interger value links for volumes.)

 

[jtbell]

I don't think there is any generally accepted answer to this question, because we don't yet have a generally accepted theory of quantum gravity.

 

[Naty1]

From the perspective of general relativity, an observer in gravitational free fall will not observe any curvature of spacetime...they observe their own local motion as a geodesic straight line. They "see" themselves as inertial, no forces evident. A distant observer stationary with respect to the gravitational source viewing that same event will also see motion along a geodesic but the geodesic is curved, reflecting acceleration of the test body.

And if I understand it correctly, a non inertial (accelerating observer) will see a different geodesic path, meaning a different acceleration, than either of the other two. This latter type is called an inertial acceleration denoting that an acceleration is observed because of the non inertial reference frame, and is independent of the physical characteristics of the "test body".
(via THE RIDDLE OF GRAVITATION, Peter Bergmann, a former student of Einstein)

Given these variations pinning down the physcial interaction might be difficult.

 

[spidey]

I am also confused with curved space time...Just because light curves does that mean space-time is curved?...Nikola Tesla has said about GR that "I hold that space cannot be curved, for the simple reason that it can have no properties. It might as well be said that God has properties. He has not, but only attributes and these are of our own making. Of properties we can only speak when dealing with matter filling the space. To say that in the presence of large bodies space becomes curved is equivalent to stating that something can act upon nothing. I, for one, refuse to subscribe to such a view"...

 

[jdstokes]

Spidey,

By definition light travels on null geodesics, which in flat spacetime are straight lines.

The fact that light travels a curved path implies that the spacetime in which the light is traveling must be curved.

James

 

[gravityblock]

Photons, and everything else, like planets, try to go where time is least. Gravity curves spacetime because the photons or anything that has mass are seeking or are pulled toward a path of least time, which is a path of more gravity. Physicists have proven with atomic clocks and airplanes that gravity slows time. Clocks run slower at lower altitudes where gravity is stronger. Time is least (flows more slowly) where gravity is most.

The Earth orbiting the sun has momentum which keeps it in orbit. If the Earth's momentum were to stop, the Earth would seek the path of least time, and be pulled straight into the sun! It would not follow a curved path to the sun if it does not have momentum.

1) Mass causes gravity.
2) Mass seeks or is pulled where time is least.
3) The larger the mass, the least time is.
4) spacetime is curved due to the curvature of the mass.
5) Without mass, time is not curved.
6) Without momentum near a mass, space is not curved.

The reason why time slows down as you approach the speed of light is because the mass increases(More mass means less time). The question I have is why does mass slow time?

This is my understanding of why gravity curves spacetime. Please correct me where I am wrong.

 

[Denton]

If i have an object flying at 99% the speed of light, it has 'less time' than the sun. So shouldn't the Earth fall straight into the flying object?

 

[atyy]

Photons, and everything else, like planets, try to go where time is least. Gravity curves spacetime because the photons or anything that has mass are seeking or are pulled toward a path of least time, which is a path of more gravity.

Massive objects take a path of greatest proper time or spacetime distance, and light takes a path of least (zero) spacetime distance, provided they are acted on by gravity alone. This is equivalent to the statement that objects take "straightest" or geodesic spacetime paths, provided they are acted on by gravity alone.

Physicists have proven with atomic clocks and airplanes that gravity slows time. Clocks run slower at lower altitudes where gravity is stronger. Time is least (flows more slowly) where gravity is most.

The time slowing down thing is usually for clocks that are not acted on by gravity alone. For example one may compare two clocks that are stationary relative to the surface of the earth. These clocks are not acted on by gravity alone, since they are prevented from falling freely by whatever is keeping them stationary. These clocks are not following spacetime geodesics.

 

[gravityblock]

@Denton: At the speed of light, length shrinks to zero and time stands still. At 99% the speed of light the object's length would be near 0 and would pass the Earth before it had time to pull the Earth into it.

 

[gravityblock]

@atyy: An atomic clock is a clock that uses the resonance frequencies of atoms as its resonator. According to Encyclopedia Britannica, the resonator is "regulated by the frequency of the microwave electromagnetic radiation emitted or absorbed by the quantum transition (energy change) of an atom or molecule." They have to constantly update the clocks on GPS satellites because they are running faster than clocks on the surface of the earth.

Einstein said that time slows down and mass increases as you approach the speed of light. Am I the only one who sees this relationship, or is my thinking curved, which could be possible. lol

 

[Denton]

@Denton: At the speed of light, length shrinks to zero and time stands still. At 99% the speed of light the object's length would be near 0 and would pass the Earth before it had time to pull the Earth into it.

Not if the Earth was going at the same speed.

 

[Naty1]

Einstein said that time slows down and mass increases as you approach the speed of light.

From the perspective a distant outside inertial observer that's correct; from the perspective of the near light speed frame observer, all appears as normal locally, but the time dilation and length contraction are seen in the frame of the outside observer. Each sees the other as moving near "c".

Massive objects take a path of greatest proper time or spacetime distance, and light takes a path of least (zero) spacetime distance, provided they are acted on by gravity alone.

That's my understanding as well.

 

[Naty1]

I don't think there is any generally accepted answer to this question, because we don't yet have a generally accepted theory of quantum gravity.

That's my take.

All the other posts are superficial explanations...which is ok, because that's all we got right now...

 

[gravityblock]

Einstein said that time slows down and mass increases as you approach the speed of light. From the perspective of a distant outside inertial observer that's correct; from the perspective of the near light speed frame observer, all appears as normal locally, but the time dilation and length contraction are seen in the frame of the outside observer. Each sees the other as moving near "c". I agree with you Naty1.

Massive objects take a path of greatest proper time or spacetime distance, and light takes a path of least (zero) spacetime distance, provided they are acted on by gravity alone. I agree with you Naty1. The reason why light takes a path of least (zero) spacetime distance is because the frequency is very high and the wavelength is very short. If you increase the mass/energy you increase the frequency and the wavelength is shorter. Massive objects takes the path of greatest spacetime distance or proper time because the energy is not as high as light and hence a longer wavelength. The frequency simply describes the number of oscillations or cycles per second, while the term wavelength describes the distance between one wave and the next. Hence wavelength and frequency are inseparably intertwined: the higher the frequency the shorter the wavelength.

Planck's formula: E=hf where:
E is the energy of a single photon,
f is the photon's frequency,
h is Planck's constant,
Einstein's formula: E=mc2 where:
E is energy,
m is mass,
c2 is the speed of light squared,
hence, hf=mc2

thus showing that the mass of a photon is directly proportional to the frequency of the photon.
E=hf and E=mc2 so hf=mc2

1)mass/energy
2)wave/particle
3)space/time
4)frequency/wavelength
5)electricity/magnetism

I believe we are saying the same thing, just looking at it from a different perspective or thought.

"The day we stop thinking, is the day we die."

 

[JesseM]

If i have an object flying at 99% the speed of light, it has 'less time' than the sun. So shouldn't the Earth fall straight into the flying object?

Velocity-based time dilation and gravity-based time dilation are two separate effects, the fact that a clock is running very slow (in whatever coordinate system you choose to use, keep in mind that different coordinate systems disagree about an object's velocity and there is no single 'true' velocity) doesn't imply it is a strong source of gravity.

 

[atyy]

@atyy: An atomic clock is a clock that uses the resonance frequencies of atoms as its resonator. According to Encyclopedia Britannica, the resonator is "regulated by the frequency of the microwave electromagnetic radiation emitted or absorbed by the quantum transition (energy change) of an atom or molecule." They have to constantly update the clocks on GPS satellites because they are running faster than clocks on the surface of the earth.

Einstein said that time slows down and mass increases as you approach the speed of light. Am I the only one who sees this relationship, or is my thinking curved, which could be possible. lol

The clock on the surface of the Earth is not falling freely.

 

[Pippo]

.... space becomes curved is equivalent to stating that something can act upon nothing...

That's not correct, nothing is exactly nothing while space is something, and gravity is a
space behaviour, distortion, in presence of bodies.

 

[gravityblock]

The clock on the surface of the Earth is not falling freely.

Clocks run slower at lower altitudes (orbits) where gravity is stronger. An atomic clock in the outer orbit of Earth will run faster than an atomic clock in the inner orbit of the earth, both clocks will be free falling.

True, False, or Speculation?

 

[atyy]

Clocks run slower at lower altitudes (orbits) where gravity is stronger. An atomic clock in the outer orbit of Earth will run faster than an atomic clock in the inner orbit of the earth, both clocks will be free falling.

True, False, or Speculation?

I don't know how to do this calculation. Usually the angular coordinates of the two clocks are set equal, but I think that's not true of free falling clocks in different radii. However the question doesn't seem like an insensible one to ask, and I'd be curious to know the answer.

 

[Naty1]

Just because light curves does that mean space-time is curved?..

Yes: That's what general relativity states via the Einstein stress-energy tensor.

space becomes curved is equivalent to stating that something can act upon nothing...

I'll bet you don't know what "nothing" means: ...(not many do; I don't) Spacetime is SOMETHING!

But the important point is that even empty space ("nothing" to some people) has quantum fluctuations, zero point energy, and maybe dark energy and dark matter. And of course no space is empty because probability waves from other portions of the universe, cosmic background radiation, gravitational fields, cosmic rays, permeate everywhere...

I even looked up "nothing" for you on Wiki: here is how they describe NOTHING: (and I agree)

In mathematics, "nothing" does not have a technical meaning. The number zero is often used interchangeably with the term. It could also be said that a set contains "nothing" if and only if it is the empty set, in which case its cardinality (or size) is zero. In other words, the word "nothing" can be an informal term for an empty set.

In physics, the word nothing is not used in any technical sense either. A region of space is called a vacuum if it does not contain any matter, though it can contain physical fields. In fact, it is practically impossible to construct a region of space that contains no matter or fields, since gravity cannot be blocked and all objects at a non-zero temperature radiate electromagnetically. However, even if such a region existed, it could still not be referred to as "nothing", since it has properties and a measurable existence as part of the quantum-mechanical vacuum.

If you'd like to "see" what spacetime MAY look like, (no guarantees) research "Penrose spin networks"...spacetime appears as a geodesic shaped with edges equivalent to areas and nodes equivalent to volumes...at the roughly Planck scale...

However, we all start off pretty much as you so don't despair..if you read Wiki on "Nothing" you'll have learned some good insights and make further progress each time you check out another aspect of physics...there are a LOT of pieces to our world...

"We know a lot; we understand little"

 

[gravityblock]

I don't know how to do this calculation. Usually the angular coordinates of the two clocks are set equal, but I think that's not true of free falling clocks in different radii. However the question doesn't seem like an insensible one to ask, and I'd be curious to know the answer.

My assumption is the clock in the lower oribt will have a higher speed than the clock in the outer orbit. Since the clock in the lower orbit has a higher speed, then it also has more energy/mass. More energy/mass equals less time. If the clocks have too much speed, then they will fly out of orbit, and if they do not have enough speed, then they will fall into the earth. The clock in the outer orbit must have a lower speed than the inner orbit clock because it would not stay in orbit at the same speed as the inner clock. This all follows the idea of e=mc2 and time is directly proportional to e=mc2. I am sure Einstein understood this, and this is how he drew his conclusions for the theory of general relativity.

Any thoughts on this assumption?

 

[atyy]

My assumption is the clock in the lower oribt will have a higher speed than the clock in the outer orbit. Since the clock in the lower orbit has a higher speed, then it also has more energy/mass. More energy/mass equals less time. If the clocks have too much speed, then they will fly out of orbit, and if they do not have enough speed, then they will fall into the earth. The clock in the outer orbit must have a lower speed than the inner orbit clock because it would not stay in orbit at the same speed as the inner clock. This all follows the idea of e=mc2 and time is directly proportional to e=mc2. I am sure Einstein understood this, and this is how he drew his conclusions for the theory of general relativity.

Any thoughts on this assumption?

To calculate the elapsed time, one integrates along the clock's spacetime trajectory, which is always possible. To get a relative rate of ticking, one needs to differentiate, not integrate, and I don't know whether that is possible or not in your scenario. Presumably this question was answered in passing for the analysis of the Hafele-Keating experiment.

 

[gravityblock]

To calculate the elapsed time, one integrates along the clock's spacetime trajectory, which is always possible. To get a relative rate of ticking, one needs to differentiate, not integrate, and I don't know whether that is possible or not in your scenario. Presumably this question was answered in passing for the analysis of the Hafele-Keating experiment.

If you add a third atomic clock that has only rest mass, then compare the other 2 orbital clocks after a specified interval of the clock that has only rest mass, I believe the clock in the lower orbit will have less time than the outer orbit clock. I need to look at the Hafele-Keating experiment to understand what you are referring too, since I am not familiar with that experiment.

Should I start a new thread? I don't want to hijack this thread.

 

[Jonathan Scott]

Clocks run slower at lower altitudes (orbits) where gravity is stronger. An atomic clock in the outer orbit of Earth will run faster than an atomic clock in the inner orbit of the earth, both clocks will be free falling.

True, False, or Speculation?

There are two effects which need to be taken into account.

For non-relativistic speeds, we can use Newtonian calculations and the following rules:

1. By GR, gravity changes clock rates by a fraction equal to the potential energy change per unit of rest energy.

2. By SR, speed slows clocks by a fraction equal to the kinetic energy per unit of rest energy.

Since lower orbits have higher speed, both of these effects combine to mean that clocks run slower in lower orbits, and hence faster in higher orbits.

For a circular orbit, v²/r = GM/r², so v² = GM/r, where M is the mass of the central body and r is the radius of the orbit (from the middle of the earth).

The kinetic energy per unit mass is v²/2, and the potential energy change per unit mass (relative to infinity) is -GM/r. For a circular orbit, this gives the well-known result that the kinetic energy is half of the (negative) potential energy relative to infinity.

This means that the overall fractional slowing of a clock, relative to infinity, for a circular orbit with radius r around a mass M is GM/rc² + v²/2c² = (3/2) (GM/rc^2).

Note that time dilation is not directly related to the "strength" of gravity (that is, the acceleration or force per unit mass) but rather to the potential, which is more like its "depth".

 

[gravityblock]

@J.S. Note that time dilation is not directly related to the "strength" of gravity (that is, the acceleration or force per unit mass) but rather to the potential, which is more like its "depth".

The rate of change of velocity is referred to as acceleration. There is no acceleration associated with the atomic clocks. The clocks have velocity but no acceleration due to gravity since they are in orbit.

The clocks in different orbits is to show that the spacetime is curved around the Earth (Do you not believe spacetime is curved due to a large mass?). It is this curved spacetime that causes an object to accelerate towards the earth. The object will only accelerate towards the Earth if the momentum is less than what is required to stay in that specific orbit that it is currently in. Momentum is the product of the mass and velocity of an object (p = mv). If the object has less momentum to stay in its current orbit then it will move to a lower orbit. Since time is less in the lower orbit then the objects mass has increased, and since the objects mass has increased, then the momentum has increased, and since the momentum has increased, then the acceleration has increased, and since the acceleration has increased, then the velocity has increased, then we move to the next lower orbit and repeat this process as long as the momentum is less than required to stay in its current orbit. This shows how and why spacetime is curved to the Earth or a large mass, also shows how and why curved spacetime causes an object to orbit the earth, also shows how and why curved spacetime causes an object to accelerate towards the Earth if the momentum is less than what is required to stay in that specific orbit, and it also answers the question I had in my first response to this thread (Why does mass slow time?).

A block hole has so much mass that time gets slower as you approach the event horizon. It is not the velocity or acceleration that causes time to slow, but it is the mass that causes time to slow. If you increase your velocity or acceleration then you increase the energy/mass for that object. Since the energy/mass has increased then time has decreased. If you are on an object and the object's rest mass is large, then time will run slower on the larger rest mass object as compared to an object that has a small rest mass.

This "time" thing is making my head hurt, lol. This is my understanding of space, time, spacetime, mass/energy, and gravity. I may be right or wrong, I don't know, but this is what makes sense to me. I have a hard time putting my thoughts into words, as most of us probably do, and this is a limitation that we all have to some degree, so please don't get caught up with words or terms that I may have used incorrectly, or where a better word or term could have been used. It is my thoughts that I am trying to project to you, so if I used a term incorrectly or a better word could have been used then please try to capture the thought I am trying to convey to you and then replace it with the correct or better term.

Does this only make sense to me? Maybe my thinking is not right.

 

[jnorman]

james - my understanding was that light travels by all possible paths. if, as you say,

how do you reconcile this comment with the results of the two slit experiments?

 

[jnorman]

btw, i think that the observations of lensing indicate that a quantum theory of gravity, based on gravitons interacting with every particle including individual photons, cannot be correct. for graviton interaction to be correct, a photon would have to follow a polygonal path as it passes a massive body, each segment of the polygon being, perhaps, of Planck length. mind-boggling, as if my mind isn't boggled enough already...

 

[Naty1]

gravity:
It appears that your most recent post, above, may base conclusions on the 1/5000 of 1% (a tiny,tiny pice) relativistic effects and may ignore the 99 plus% posted by Jonathan. In other words, classical conditions prevail here and general relativity contributions are insignificant. I can suggest that if the logic is clear to you the words are unclear to me.

 

[gravityblock]

gravity:
It appears that your most recent post, above, may base conclusions on the 1/5000 of 1% (a tiny,tiny pice) relativistic effects and may ignore the 99 plus% posted by Jonathan. In other words, classical conditions prevail here and general relativity contributions are insignificant. I can suggest that if the logic is clear to you the words are unclear to me.

There is no need to bring quantum mechanics into this because this can be explained by GR and SR. I do not feel that general relativity contributions are insignificant here, and even Jonathon used both GR and SR in his post.

I agree with what Jonathon said. This supports my idea that at higher speeds time run slower because the energy/mass is more for that object. It also means that 2 object's with different rest mass will experience a different time. Most of what Jonathon said is about how to calculate the mass of an object, kinetic energy and potential energy change per unit mass which is all in GR and SR. So what is the 99% of what Jonathon said that I ignored?

Maybe if we ask ourselves these questions it will become clearer.

1) When an object is orbiting the earth, then why does it not accelerate as it is orbiting?
2) When an object is not orbiting the Earth but falling through to lower orbits then why does it accelerate?

In both questions the objects are under the influence of gravity or the Earth's mass/energy, but you have different effects as far as acceleration is concerned.

My answer to question 1 is this: The object does not accelerate because the path that the object is following around the Earth has the same curved time and the same curved space. A lower orbit will have a different curved time and a different curved space, etc.

question 2: The object will accelerate as it is falling through to lower orbits because there is a different curved time along the path that it is falling through. It is the space/time difference, that causes the object to accelerate if it doesn't have enough momentum to stay in that orbit.

When we see an object that curves along its trajectory path due to a large mass, then we are able to see that the space is curved. When we see an object that accelerates towards a large mass, then we are able to see how time is curved, we see the time being curved in the acceleration of the object.

Most of my posts have been redundant, I have been saying the same thing in most of my posts, just in a different way. I do not like redundancy and I'm sure you feel the same way. I will not touch on this idea anymore unless I see it has some support.

I guess if this doesn't help you or other people to see the logic in my thoughts, then I must be wrong in my thinking, which wouldn't be the first time.

They say, "If you break your leg, be thankful you have a leg to break"

 

[atyy]

1) When an object is orbiting the earth, then why does it not accelerate as it is orbiting?
2) When an object is not orbiting the Earth but falling through to lower orbits then why does it accelerate?

Suppose gravity is the only force the object feels.

In Newtonian gravity, considering 3-acceleration:
1) It accelerates as it orbits
2) It accelerates as it falls

In Einstein gravity, considering 4-acceleration:
1) It does not accelerate as it orbits
2) It does not accelerate as it falls