Erik's Paradox: Exploring GR & the Gravity Effect

[ErikThePhysicist1]

TL;DR Summary

There is a problem with GR and it involves light. We do not know yet if the conjecture is true.

I believe me and my family have found a problem with GR in the context of the explanation of the "Gravity Effect". If Gravity is not a force, but it is rather caused by the linear acceleration of bodies through space-time, rather than the attraction between bodies, shoudn't this acceleration reach light speed sooner or later?

If you have been accelerating for 1 year ( at 9.8㎨ (= 309,092,000㎧ speed)), then you should travel faster than light (c = 299,792,458㎧), and you should turn into energy completely at the 1 year mark. In the case of the Earth, since it is 4,500,000,000 years old (1.3907376e+18㎧ or 4639001292.02c) shouldn't it have reached light speed so long ago?

This is a weird problem in GR and we are trying to contact scientists/smart people that we know/found to tell them about this paradox/conjecture/contradiction. Please comment if you have a theory. Thank you.

 

[FactChecker]

Before GR, there was SR (Special Relativity). That described how measurements of time and space change as you travel faster and faster. It stops you from doing what you said because the meaning of "a year" changes and the meaning of "a meter" changes. One interesting introduction to these concepts is in George Gamow's book "Mr Tompkins in Paperback". It might be too mathematical for you now, but it is the most accessible that I am aware of.

 

[ErikThePhysicist1]

Before GR, there was SR (Special Relativity). That described how measurements of time and space change as you travel faster and faster. It stops you from doing what you said because the meaning of "a year" changes and the meaning of "a meter" changes. One interesting introduction to these concepts is in George Gamow's book "Mr Tompkins in Paperback". It might be too mathematical for you now, but it is the most accessible that I am aware of.

Brilliant observation, thank you, but gravity curvature of space does not contract (Contraction caused by SR) and it has infinite energy. So this observastion will not completely work out. Do you have any other ideas? This observation will at least work out a bit, but not completely.

 

[Dale]

Summary:: There is a problem with GR and it involves light. We do not know yet if the conjecture is true.

I believe me and my family have found a problem with GR.

Whenever you believe this you can know with certainty that you have found a problem in your understanding, not a problem in relativity.

If you have been accelerating for 1 year ( at 9.8㎨ (309,092,000㎧ speed), then you should travel faster than light (c = 299,792,458㎧), and you should become energy completely at the 1 year mark

There are two types of acceleration. The first is called “proper acceleration”. This is the type of acceleration that you actually feel. It is the acceleration measured by an accelerometer. The second is called “coordinate acceleration”. This is the rate of change of your velocity with respect to some set of coordinates. It depends on the coordinates you use.

In Newtonian physics in an inertial frame the proper acceleration and the coordinate acceleration are the same, but that is not true in relativity. In relativity in an inertial frame the proper acceleration is only equal to the coordinate acceleration for low speeds. As the speed increases the coordinate acceleration becomes less than the proper acceleration.

Thus, as you maintain a constant 1 g proper acceleration (which you can do indefinitely in principle), your coordinate acceleration becomes less and less with respect to an inertial frame. Your coordinate acceleration approaches zero as your speed approaches c, so your speed never exceeds c in any inertial frame.

Now, for the earth, our typical coordinates are non-inertial. So we can (and do) have proper acceleration without any coordinate acceleration, even at low speeds. Thus in our typical non-inertial Earth coordinates we don’t even approach relativistic speeds, let alone c.

 

[Frabjous]

Welcome to physicsforums!

In physics, velocity has a magnitude and a direction. An acceleration can change either or both of them. We use vectors to describe it.
While you feel a force due to the gravity of the earth, you also feel a force due to the ground which cancels out the force due to gravity. This is why you do not fall through the floor.

The Earth feels acceleration from the sun, but in this case it changes the direction that the Earth moves in. This is why the Earth orbits around the sun.
The speed of light is much greater than anything you will normally experience. It is only when you get close to it (or near something very massive) that you begin to observe the relativistic effects that the other posters have mentioned. Having to think beyond your normal experience is part of what makes relativity interesting.

 

[sysprog]

Before GR, there was SR (Special Relativity). That described how measurements of time and space change as you travel faster and faster. It stops you from doing what you said because the meaning of "a year" changes and the meaning of "a meter" changes. One interesting introduction to these concepts is in George Gamow's book "Mr Tompkins in Paperback". It might be too mathematical for you now, but it is the most accessible that I am aware of.

Gamow's One, Two, Three, Infinity provides a very good introduction to relativity while requiring no more mathematics than some basic geometry.

 

[sysprog]

Brilliant observation, thank you, but gravity curvature of space does not contract (Contraction caused by SR) and it has infinite energy. So this observastion will not completely work out. Do you have any other ideas? This observation will at least work out a bit, but not completely.

What are you trying to say when you use the term 'infinite energy'??

 

[ErikThePhysicist1]

What are you trying to say when you use the term 'infinite energy'??

i mean to say that it is not really a thing so there is not really meaning to energy and energy cost to it. (it = curvature of space)

 

[ErikThePhysicist1]

In physics, velocity has a magnitude and a direction. An acceleration can change either or both of them. We use vectors to describe it.
While you feel a force due to the gravity of the earth, you also feel a force due to the ground which cancels out the force due to gravity. This is why you do not fall through the floor.

The Earth feels acceleration from the sun, but in this case it changes the direction that the Earth moves in. This is why the Earth orbits around the sun.
The speed of light is much greater than anything you will normally experience. It is only when you get close to it (or near something very massive) that you begin to observe the relativistic effects that the other posters have mentioned. Having to think beyond your normal experience is part of what makes relativity interesting.

I know + That is not related to the conjecture.

 

[sysprog]

i mean to say that it is not really a thing so there is not really meaning to energy and energy cost to it. (it = curvature of space)

I suggest that you maybe should read some primers and watch some videos and then maybe look at one of the standard introductory texts, e.g. Robert Resnick's "Introduction to Special Relativity" $-$ https://archive.org/details/robertresnickintroductiontospecialrelativitywiley1968

 

[strangerep]

[Gravity] is rather caused by the linear acceleration of bodies through space-time, [...]

It's not. Gravity, i.e., curvature of spacetime, is caused by the presence of energy-stress-momentum. This error invalidates the intent in the rest of your post #1.

Aside: you (and your family?) seem not to have read the PF guidelines (you were given an opportunity to do so when you created your account). In particular, personal speculative theories are not a suitable subject for discussion here . Several knowledgeable people have cut you some slack in this thread because you said you're 8 yrs old. But it's time for you to go back and read the PF guidelines properly. They can be found under the "Info" tab on the PF homepage, then "Terms and Rules".

It's ok, of course, to seek clarification/correction of misunderstandings. But for that to be most effective, you should tell us what relevant textbooks you have studied. (I'm guessing the answer is "none"?) But you marked this thread "I" level rather than "B" level which suggests you want an answer pitched at university undergrad level.

 

[sysprog]

@A.T. posted this in another thread:

 

[jedishrfu]

Einstein did Gedanken (thought) experiments to understand reality. So often laypeople feel they can do them too without any need for math. Sadly, though Einstein was well versed in math and physics and was able to steer clear of things that could derail his understanding.

In contrast, laypeople try to figure things out using their understanding of words not realizing that the words are based on math and it's the math you need to work through with along the key physics insight to answer your questions.

Several posters here have recommended some good popular science books to read but they will only get you so far and as @Dale has said it's your understanding of relativity that needs to be adjusted not the physics.

One recent book from Amazon may help with your understanding:

https://www.amazon.com/dp/0465023312/?tag=pfamazon01-20

make sure to listen to the audio clip from the author on the page describing his book. It's just wonderful.

It might even help to get the audio version of the book although I don't know if the author does the audio or not.

Check out Ben Crowell's online books on physics including the one Relativity for Poets which you might find interesting.

https://www.lightandmatter.com/

https://www.lightandmatter.com/poets/

 

[PeterDonis]

If Gravity is not a force

In GR this is true, yes, gravity is not a force.

but it is rather caused by the linear acceleration of bodies through space-time

This, however, is not true in GR. Gravity in GR is a manifestation of spacetime curvature. "Linear acceleration of bodies through spacetime" is not a valid description of spacetime curvature.

You might be getting confused here by common presentations of the equivalence principle, which says that locally, standing inside a rocket that is accelerating at 1 g through empty space is not distinguishable from standing in a room on the surface of the Earth and feeling an acceleration of 1 g. However, that qualifier, locally, is crucial. It means not only locally in space (you can't look outside the rocket or the room but can only make measurements inside), but locally in time (if you are allowed to make measurements over a long enough time, you can spot effects of spacetime curvature being present on Earth that are not present in an accelerating rocket in empty space). The "locally in time" part means that looking at what a rocket does if it accelerates in empty space over along period of time (for example, after 1 year it will be moving at close to the speed of light relative to an object that remained at rest at its starting point) is irrelevant to understanding the effects of gravity.

 

[PeterDonis]

If you have been accelerating for 1 year ( at 9.8㎨ (= 309,092,000㎧ speed)), then you should travel faster than light (c = 299,792,458㎧)

Note that in relativity this is not the case. A good quick reference for the correct behavior of an accelerating rocket in relativity is the Usenet Physics FAQ article on the relativistic rocket equation:

https://math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html

you should turn into energy completely at the 1 year mark.

In relativity, objects that move slower than light (and have nonzero rest mass) are fundamentally different from objects that move at the speed of light (and have zero rest mass). One cannot turn into the other just by accelerating.

Also, your implicit description of objects moving at the speed of light as "turning into energy" is not correct. "Energy" is a general concept and all objects have energy, whether they have nonzero rest mass or zero rest mass.

 

[PeterDonis]

gravity curvature of space does not contract (Contraction caused by SR)

Length contraction in SR is a kinematic effect due to switching reference frames. It has nothing to do with spacetime itself contracting.

Also, in GR, gravity is curvature of spacetime, not space. They are not the same thing.

and it has infinite energy.

This is not correct; curvature of spacetime does not have infinite energy.

So this observastion will not completely work out. Do you have any other ideas? This observation will at least work out a bit, but not completely.

You are being very overconfident here. I realize this is a new subject for you and you are not yet aware of how much you do not know about it. But in that situation, you should be less confident in anything you believe about the subject, not more. As @Dale has already pointed out, it is overwhelmingly likely that it is you who are making a mistake somewhere. That should not prevent you from asking questions, and continuing to ask further questions about the responses you get if something in them doesn't make sense to you, but it should prevent you from dismissing people's responses out of hand as you do in the quote above.

 

[PeroK]

First, to clarify the "conjecture":

1) I am sitting on the surface of the Earth. There is a real upward force of $mg$ acting on me from the ground, which implies an absolute (proper) upward acceleration of $g$.

2) After a time of $t$ I must have increased my speed in the upward direction by $gt$.

The first observation is that 2) fails as a conjecture. There is no measurable increasing upward speed. Not as measured from the surface of the Earth; not as measured from the rest frame of the Solar system; and, not as measured by a hypothetical interstellar or intergalactic observer.

Let's try an alternative conjecture that satisfies the observed data:

2) Absolute (proper) acceleration does not imply the concept of absolute motion. In other words, just because there is a constant proper acceleration does not imply there must be constant increasing speed in that direction in some absolute sense.

That sounds more like a conjecture worth considering!

 

[Dale]

Several off topic posts were deleted. The poster's age is irrelevant and has been removed from the title and the thread discussion.

 

[jedishrfu]

Veritaseum (an element of truth) posted this video last year on youtube that may be of interest to you. It explains why gravity is not a force.



and minutephysics series on SR:





Veritaseum, MinutePhysics, SmarterEveryDay are some great channels that discuss science and engineering topics. 3blue1brown discusses mathematics with great visualizations and insight.