A dumb GR question.

[xelasnave]

If mass bends space such to manifest gravity would this not suggest that if we drop two objects from as high as possible then the greater mass could be expected to accelerate faster than the one with less mass.

Mass bends space so the one with the greater mass should bend space more one could think???and so create greater gravity.
If GR allows objects of different mass to accelerate at the same rate irrespective of mass does this not contradict the main premise of GR?

Also if frame dragging is a fact will not such a premise be born out in the trajectory of the falling object?
Thank you
alex

[renormalised (Carl)]

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

No, the acceleration of the object, regardless of its mass, is entirely due to the spacetime curvature in which it is falling...neglecting air resistance and such, all objects, whether they weight 1 gram or a million will fall in Earth's gravitational field/spacetime curvature (for example), at 9.81m/s^2. As they will also fall at a constant rate (given that the field curvature doesn't go off the scale, like in a black hole), in whatever gravitational field they find themselves in. So, a 1 gram object, will fall at the same rate as a 1 million gram object. Both will hit the ground at the same time. GR is not contradicted at all. All GR is saying is that you cannot tell the difference between a gravitational field produced via acceleration or naturally occurring spacetime curvature. Since sitting on the Earth's surface, you are experiencing an acceleration towards the body of the Earth of 1g (9.81m/s^2), GR is entirely correct in its assumptions. Hop in your car and slam the foot down on the accelerator...accelerate at roughly 19.5m/s^2 and you'll feel the force of 2g's pushing you into the back of your seat. Then go to a planet with that gravitational pull....you'll feel exactly the same, twice as heavy as you normally would feel.

Frame dragging will cause a minute change in the trajectory of the falling object, for most gravitational fields. Only in extreme cases around objects like neutron stars and black holes will you get enough frame dragging to cause an appreciable change in the trajectory of the falling objects.

[xelasnave]

Thank you Carl for your reply.
What I dont get is why an object with 1,000,000 grams mass does not bend space more than one of 1 gram mass... and therefore cause a different "bend" and a greater gravity in effect.
I took some time to try and understand some lectures (particularly the math) and can see how mass cancels in the Newtonian approach but must have missed something that causes me to raise the question here.

Thank again.
alex

[renormalised (Carl)]

It does bend space a little more, but the effect is so small that it only becomes important on very large scales...like planetary size and greater. However, if you were to drop Jupiter and the Earth into the Sun, they would both fall into it at the same acceleration if they were dropped from the same height/distance. Both would hit at the same time. Just to show you, get a glass and an USB stick, stand over a soft chair or sofa, hold both at about the same height, then drop them into the chair. You'll see they both hit the chair at roughly the same time. Now, vary which one is further away from the chair and repeat the experiment, see what you get and come back here to report what you see

[bojan]

Originally Posted by renormalised

.... get a glass and an USB stick, stand over a soft chair or sofa, hold both at about the same height, then drop them into the chair....

Just make sure the glass is empty

[mbo (Pat and Kirk)]

OK, I'll rephrase the question, if I get a marble and place it 200,000 K's from the earth, stationary with respect to the sun, i.e not in earths orbit, and time it till point of impact on the earth (Ignoring the atmosphere and friction), and I then repeat the experiment replacing the marble with Venus, will I get a smaller time to impact because of their mutual attraction?
If the Earth in the previous example were some how fixed (stapled to space) and therefore couldn't move toward venus, would the same time to impact be observed
And for a follow up, could you give me a mind picture of the warped spacetime involved :-)

[xelasnave]

Originally Posted by renormalised

It does bend space a little more, but the effect is so small that it only becomes important on very large scales...like planetary size and greater. However, if you were to drop Jupiter and the Earth into the Sun, they would both fall into it at the same acceleration if they were dropped from the same height/distance. Both would hit at the same time. Just to show you, get a glass and an USB stick, stand over a soft chair or sofa, hold both at about the same height, then drop them into the chair. You'll see they both hit the chair at roughly the same time. Now, vary which one is further away from the chair and repeat the experiment, see what you get and come back here to report what you see

Thank you for posting a very helpful reply.

With respect Carl terms such as " a little more" and "so small" make me feel I have made a reasonably valid point, however it is not science unless we are specific in quantifying how much "a little more" and "so small" represents by measurement (conducted upon many samples) but I suspect in relation to the 1 gram v the 1,000,000 gram question that any measurement presumably would be beyond the capabilities of current human endeavour ...although when I read articles announcing that GR has been "proved" to operate even at measurements as low as billionths of an inch I do wonder if there is any limit on our ability to observe "small"...

I think that the glass and the chair etc suggestion leaves us with a rather slack experiment ... holding the objects at about the same height offends my desire to eliminate areas that could corrupt any observation..we need to drop from exactly the same height.and as to both hitting at "roughly the same time" this is far to loose as we need to know if they hit at exactly the same time or not at exactly the same time.

However your suggestion there is benefit in observing what actually does happen appeals greatly to my "learn by observation" approach to the universe and in this regard I propose that it is only by dropping our two test objects from a great height and observing what actually happens and taking great care not to have a preconceived view of the outcome...that we can know for sure.

I guess the point I am making that the observations we take with absolute acceptance..namely that irrespective of mass objects fall at the same rate.. could reasonably be regarded as suspect ...and that observations conducted where objects fall over greater distances should be made and the results analyzed.

I look at the matter in this way because my understanding of the general premise given to us by GR ...that mass alters space time and it is this relationship that we currently express as gravity... although what it seeks to do is simply describe a relationship between frames of reference ..and I think that is what you pointed out in your reply.

AS you pointed out GR has an element of "what the observer experiences" however it seems to me that we have to fit the general premise into a reality suggested by it...or as difficult as it may seem to except it could be that our fundamental "belief" that things fall a the same rate irrespective of mass was never put to a reasonable test (involving the distances GR would need) and the results observed. Observation over a chair or from the tower at Pizza may not be grand enough to demonstrate the belief may be flawed.



Certainly we can say things fall at the same rate if we observe only over relatively small distances, as no doubt we have been restricted to) and I suspect that if any differences in the rate of fall have been observed the difference was simply put down to air resistance or whatever because we already know things fall at the same rate...

So if we are to be sure of what happens we need to drop the test articles from a great distance and mask out things that may corrupt the result..air resistance for example...

I submit that such an experiment may show our current belief to be flawed even if only just a little

alex

[bojan]

Originally Posted by xelasnave

... our fundamental "belief" that things fall a the same rate irrespective of mass was never put to a reasonable test (involving the distances GR would need) and the results observed. Observation over a chair or from the tower at Pizza may not be grand enough to demonstrate the belief may be flawed.

Alex, this is not a "belief" but the fact, proven experimentally many, many times.. and not from the couch perspective.
The calculated and observed orbital movements of the planets (Mercury in particular) around the Sun is only one of the experiments I am talking about.
"Free fall" to the Sun is only the special case of orbital motion around it.

[Robh (Rob)]

I am inclined to Alex's view here. That two bodies do not in fact fall with the same acceleration. Consider this case (mind games)...
The Earth is "dropped" into the Sun, it falls into the Sun in a manner largely dependent on the mass of the Sun. One zapped Earth.
A star of 100 solar masses is "dropped" into the Sun. The Sun accelerates towards the large star in a manner more dependent on the large star's mass. One zapped Sun.

Now consider some maths.
F = GMm/r^2 is the force between two bodies mass M and m.
What is the acceleration of m towards M?
F = ma1 = GMm/r^2
a1 = GM/r^2
However, there is also an acceleration of M towards m.
F = Ma2 = GMm/r^2
a2 = Gm/r^2
Does this not mean the combined acceleration is in fact
a1+a2 = GM/r^2+Gm/r^2 = G(M+m)/r^2

For a small body m, the acceleration would approximate to GM/r^2 without measurable difference. However, for larger bodies e.g. m = M the acceleration will increase substantially.

Regards, Rob.

[bojan]

In case of two bodies (of comparable masses), the acceleration on each one of them will be towards the point between them (centre of gravity) as if the combined mass of both is concentrated there.
The acceleration will of course be dependent of the total mass of the system.. but this will in no way put GR in question, as suggested by Alex.

The point I am trying to make is (and I know there are people on this forum who will absolutely hate me because of this) is, a myriad of scientists were involved in questioning and answering this and similar dilemma.. Alex, you are not the first, and not the last. But, some reading of the basics of physics would help you to understand those things better/correctly.

[sjastro]

Originally Posted by Robh

I am inclined to Alex's view here. That two bodies do not in fact fall with the same acceleration. Consider this case (mind games)...
The Earth is "dropped" into the Sun, it falls into the Sun in a manner largely dependent on the mass of the Sun. One zapped Earth.
A star of 100 solar masses is "dropped" into the Sun. The Sun accelerates towards the large star in a manner more dependent on the large star's mass. One zapped Sun.

Now consider some maths.
F = GMm/r^2 is the force between two bodies mass M and m.
What is the acceleration of m towards M?
F = ma1 = GMm/r^2
a1 = GM/r^2
However, there is also an acceleration of M towards m.
F = Ma2 = GMm/r^2
a2 = Gm/r^2
Does this not mean the combined acceleration is in fact
a1+a2 = GM/r^2+Gm/r^2 = G(M+m)/r^2

For a small body m, the acceleration would approximate to GM/r^2 without measurable difference. However, for larger bodies e.g. m = M the acceleration will increase substantially.

Regards, Rob.

The forces on the two bodies are equivalent. Newton's third law in action.

Regards

Steven

[Robh (Rob)]

Originally Posted by bojan

In case of two bodies (of comparable masses), the acceleration on each one of them will be towards the point between them (centre of gravity) as if the combined mass of both is concentrated there.
The acceleration will of course be dependent of the total mass of the system.. but this will in no way put GR in question, as suggested by Alex.

I agree. If anything, it blends in quite well with the concepts of GR.

Regards, Rob.

[Robh (Rob)]

Originally Posted by sjastro

The forces on the two bodies are equivalent. Newton's third law in action.

Regards

Steven

Agreed. The forces are equal.
But the accelerations are not.

Regards, Rob.

[xelasnave]

Originally Posted by bojan

Alex, this is not a "belief" but the fact, proven experimentally many, many times.. and not from the couch perspective.
The calculated and observed orbital movements of the planets (Mercury in particular) around the Sun is only one of the experiments I am talking about.
"Free fall" to the Sun is only the special case of orbital motion around it.

Yes but has any experiment been done as I suggest is my point.. we believe it has been done and those doing it are right etc...but has anyone observed what I suggest...if not may I ask what specific observation we should rely upon?

AND this part is in reply to your later post suggesting I am trying to call GR into question ..I am studying it to understand it not to destroy it...I am not calling GR into question...no it is the basis we conclude that all objects fall at the same rate that I question..and I question thus because of the premise (reasonable at that) that it is mass that bends space ....it is my concern that GR tells us the rate should vary and I believe that if we did an experiment such as suggested GR would win out and perhaps identify mass is relevant to the falling rate...Does not GR's prediction as to Mercury point to something along the lines I suggest...By the way I dont know the answer but certainly the prediction was not in line with the then expectations an observation of Mercury would provide.

But to affirm the point... I am not attempting to bring down GR but if anything point out something it suggests to me but perhaps not to others.
Remember DrA along with Leonardo and Newton are my most favorite heros.

Also when I bag inflation ...it is inflation that I bag (rather than generally big bang) as I think there are other answers we will miss because simply accepting the premise of inflation means that other options will never be investigated.... Inflation was needed to fix an objection with the big bang but perhaps it was unsatisfactory... to me it is unsatisfactory and I dont care what math Mr Guth enlists as proof...it seems entirely unacceptable that all we have.. absolutely everything everywhere was created in under 30 seconds and I would rather an alternate that is not totally offensive to reason..

Does such an opinion mean I dont buy big bang...no I simply feel we have taken the wrong path..the big bang Universe may be older etc. and given Hubble Deep sky captures showing a universe seemingly older than it should be..why not... but I will still entertain a big bang without inflation irrespective of the difficulties excluding the notion of inflation may leave us with...

But please I am not on a mission to destroy everything but simply have concerns which happily I am able to air here. Add to that I dont know much about any of this I have dumb questions...

We need more beer if I am to go deeper into this aspect of course. AND you should be happy to hear that I have been really concentrating on doing math but yet my view of it being more than supporting evidence in any matter has not changed...
alex

[xelasnave]

Originally Posted by Robh

I am inclined to Alex's view here. That two bodies do not in fact fall with the same acceleration. Consider this case (mind games)...
The Earth is "dropped" into the Sun, it falls into the Sun in a manner largely dependent on the mass of the Sun. One zapped Earth.
A star of 100 solar masses is "dropped" into the Sun. The Sun accelerates towards the large star in a manner more dependent on the large star's mass. One zapped Sun.

Now consider some maths.
F = GMm/r^2 is the force between two bodies mass M and m.
What is the acceleration of m towards M?
F = ma1 = GMm/r^2
a1 = GM/r^2
However, there is also an acceleration of M towards m.
F = Ma2 = GMm/r^2
a2 = Gm/r^2
Does this not mean the combined acceleration is in fact
a1+a2 = GM/r^2+Gm/r^2 = G(M+m)/r^2

For a small body m, the acceleration would approximate to GM/r^2 without measurable difference. However, for larger bodies e.g. m = M the acceleration will increase substantially.

Regards, Rob.

Thanks for your post Rob I feel less foolish in suggesting something we take as a given may not be that way at all.

alex

[xelasnave]

F=MA does it not?
does this mean M = F/A and A = F/M ...how can we get a valid result if we dont drop something on something...as in the A=F/M we can replace F with MA which cancels out M leaving A=A ...
alex

[bojan]

Originally Posted by xelasnave

Yes but has any experiment been done as I suggest is my point.. we believe it has been done and those doing it are right etc...but has anyone observed what I suggest...if not may I ask what specific observation we should rely upon?

Well, sometimes you can't have experiment in a pure form, like you described...
But, there are "equivalent" situations (like Mercury's orbit), from where we can "extract" the desired information (together with some unwanted one).
Or, close pulsars, for example.. if their observed behaviour corresponds to specific theoretical ideas, you can safely apply the same theory to your specific experiment.
In time you might even find a real situation, sufficiently close to your ideal experiment.

[CraigS]

Originally Posted by xelasnave

Also when I bag inflation ...it is inflation that I bag (rather than generally big bang) as I think there are other answers we will miss because simply accepting the premise of inflation means that other options will never be investigated.... Inflation was needed to fix an objection with the big bang but perhaps it was unsatisfactory... to me it is unsatisfactory and I dont care what math Mr Guth enlists as proof...it seems entirely unacceptable that all we have.. absolutely everything everywhere was created in under 30 seconds and I would rather an alternate that is not totally offensive to reason..


alex

Who says "that there are other answers we will miss because simply accepting the premise of inflation means that other options will never be investigated" ?

Seems to me there is lots of investigation/query into it and all that surrounds it.

Also, it's not just math that gives rise to the principle of Inflation.

Whether Inflationary BBT is offensive to reason or not is no reason to discard it !

My 2 cents worth.

Cheers

[bojan]

Originally Posted by CraigS

Whether Inflationary BBT is offensive to reason or not is no reason to discard it !

Exactly right.

BTW, "common sense" as accepted by majority of (uneducated) people is not the same thing as "Common sense" found among people who are actually experts into specific field of science or technology or whatever.

Unfortunately (for many of us), sometimes we simply have to accept certain things.. because we can't comprehend them or we do not have time to get deeper into them.

[CraigS]

Originally Posted by bojan

Exactly right.

BTW, "common sense" as accepted by majority of (uneducated) people is not the same thing as "Common sense" found among people who are actually experts into specific field of science or technology or whatever.

Onfortunatelly, sometimes we simply have to accept certain things.. because we can't comprehend them or we do not have time to get deeper into them.

Yep and even experts don't have a single "common sense".