Weightless in a Shielded Room: Does Gravity Still Apply?

[whybother]

Yeah well, Newtonian gravity is highly inaccurate compared to Einsteinian relativity, just like Euclidean geometry is highly inaccurate compared to Riemannian geometry. Euclidean geometry deals with the geometry of planes, which are flat. Absolutely nothing is flat in this world; some things may look flat to the naked eye. But if you look at the clusters of atoms that make up, let's say, a table, you will see that it is very rough, and in turn, very curved at the molecular level. Riemannian geometry is has been the "geometry of spacetime." Riemannian geometry is for curvature (spacetime is curved). Einstein used Riemmanian geometry as his mathematical tool for relativity.

I'm sorry, but are you kidding? "Euclidean geometry is highly inaccurate compared to Riemannian geometry"? No, not inaccurate... just used for different purposes. Things being 'curved' at the molecular level doesn't mean Euclidean geometry is invalid or doesn't have it's purpose - especially when most of the time you are taking about 2-curvature embedded in a flat 3D Euclidean space...

 

[dendros]

Hello, I am passionate about physics and I'd like some clarification: is it true that in the General Theory of Relativity the speed of light is no longer a constant (in magnitude)?

 

[A.T.]

Hello, I am passionate about physics and I'd like some clarification: is it true that in the General Theory of Relativity the speed of light is no longer a constant (in magnitude)?

The speed of light in vacuum is locally still constant.

Actually it is only if you assume a flat space-time, you will come to the conclusion that light is slowed down by masses. But the curvature of space-time stated by GR prevents exactly that. It makes sure that locally it is still constant.

 

[dendros]

The speed of light in vacuum is locally still constant.

Actually it is only if you assume a flat space-time, you will come to the conclusion that light is slowed down by masses. But the curvature of space-time stated by GR prevents exactly that. It makes sure that locally it is still constant.

Hello. Thank you for your answer. If the speed of light is locally constant, how about globally: also constant (same magnitude as locally), or variable? That's what I'd like to know, because from Einstein's book "On the Special and General Theory of Relativity (A Popular Account)" I understood that the speed of light was variable (different from the local magnitude) globally.

 

[Dale]

The coordinate speed of light is not constant, even in flat spacetime in non-inertial reference frames. Coordinate speeds are relative to a specific coordinate system.

However, what is coordinate independent is the light cone. In other words, if you have a flash of light at some event, all coordinate systems will agree on the set of events that receive that flash. Geometrically that is the set of all events with a spacetime interval of 0 from the flash.

In local inertial reference frames the two statements "the speed of light is constant" and "all frames agree on the light cone" are equivalent. In other frames the latter is still true although the former is not. So the frame invariance of the light cone is more fundamental in that sense.

 

[DrGreg]

Hello. Thank you for your answer. If the speed of light is locally constant, how about globally: also constant (same magnitude as locally), or variable? That's what I'd like to know, because from Einstein's book "On the Special and General Theory of Relativity (A Popular Account)" I understood that the speed of light was variable (different from the local magnitude) globally.

To expand on what DaleSpam said, speed is measured relative to a frame of reference. The speed of light is constant when measured in an inertial reference frame, but not necessarily in other frames. An inertial frame is one relative to which free-falling objects move at constant velocity.

In special relativity, inertial frames fill the whole of spacetime, so the speed of light, measured in any inertial frame, is constant everywhere. (But not so in non-inertial frames.)

In general relativity, there are no such things as global inertial frames, but there are "local inertial frames", i.e. frames that are good approximations to inertial frames within a small enough region around the free-falling observer. In these frames the speed of light always takes the same value at the location of the observer. But when you try to extend such a frame over a larger area, it becomes non-inertial; gravitational tidal effects cause free-falling objects (that are not near the observer) to accelerate relative to the frame, and the speed of light may vary.

So a free-falling observer always measures the same value locally for the speed of light, but not at a distance from the observer.

 

[dendros]

Thanks for the explanation. I want to know if the speed of light in GR may be outdated, if it is constant?

 

[DrGreg]

Thanks for the explanation. I want to know if the speed of light in GR may be outdated, if it is constant?

Sorry, I've no idea what you mean by "outdated" in this context. Can you ask your question with different words?

 

[George Jones]

In general relativity, there are no such things as global inertial frames, but there are "local inertial frames", i.e. frames that are good approximations to inertial frames within a small enough region around the free-falling observer. In these frames the speed of light always takes the same value at the location of the observer.

And in local non-inertial frames, too!

So a free-falling observer always measures the same value locally for the speed of light, but not at a distance from the observer.

All observer's, relative to their own local frame measure the same value for the speed of light.

For example, non-inertial observers that hover above a Schwarzschild black hole all measure c to be the local speed of light relative to their frames.

 

[dendros]

Sorry, I've no idea what you mean by "outdated" in this context. Can you ask your question with different words?

Sorry. Not speaking English, are from Romania, I used Google translator to post. I wanted to know if is possible in GR speeds greater than light speed.

 

[Dale]

I wanted to know if is possible in GR speeds greater than light speed.

No, it is not possible to travel faster than light (spacelike worldline) at any point in GR. However, it is theoretically possible to take a shorter path through spacetime and arrive before light that took the longer path.

 

[dendros]

Oh, I understand. From a theoretical point of view, you can create a shortcut through space-time? I understand that in GR space is equivalent to the gravitational field.

 

[D H]

Yeah well, Newtonian gravity is highly inaccurate compared to Einsteinian relativity

Where? In the vicinity of a black hole? General relativity predicts a paltry 43 arcseconds/century anomalistic precession that Newtonian gravity doesn't explain. This is fairly tiny compared to Mercury's mean motion of 538,091,702 arcseconds/century. The impact of relativity on planets other than Mercury is smaller yet. Other than GPS (relativity is very important when it comes to GPS), spacefaring nations use good old Newtonian gravity to model the motions of their spacecraft for the simple reason that Newtonian gravity is just as accurate as a full-blown relativistic model. The errors from using Newtonian gravity is orders of magnitude smaller than the errors induced by imperfect sensors and effectors.

 

[dendros]

On the forum of Romania have submitted an idea that I do not know if original or not.
In this idea, I imagine the space as equivalent to all the many fields in the Universe (not just with the gravity field, as in GR).
This equivalence understand the meaning that each field is a component, an aspect of space, and many these issues is what we call space, in the most general sense.
And so I said it could be possible speeds grater than c, if there are fields in which the energy (and implied mass) could transmit (move) with higher speeds than the speed of light in vacuum.
Maybe the idea is just silly, but present here, to clarify definitively whether so or not.

 

[George Jones]

On the forum of Romania have submitted an idea that I do not know if original or not.
In this idea, I imagine the space as equivalent to all the many fields in the Universe (not just with the gravity field, as in GR).
This equivalence understand the meaning that each field is a component, an aspect of space, and many these issues is what we call space, in the most general sense.
And so I said it could be possible speeds grater than c, if there are fields in which the energy (and implied mass) could transmit (move) with higher speeds than the speed of light in vacuum.
Maybe the idea is just silly, but present here, to clarify definitively whether so or not.

As they stand, your ideas look to fuzzy to be meaningful. Also, Physics Forums is meant for the discussion of mainstream physics ideas. From the Physics Forums rules,

Overly Speculative Posts:
One of the main goals of PF is to help students learn the current status of physics as practiced by the scientific community; accordingly, Physicsforums.com strives to maintain high standards of academic integrity. There are many open questions in physics, and we welcome discussion on those subjects provided the discussion remains intellectually sound. It is against our Posting Guidelines to discuss, in most of the PF forums or in blogs, new or non-mainstream theories or ideas that have not been published in professional peer-reviewed journals or are not part of current professional mainstream scientific discussion.

 

[dendros]

As they stand, your ideas look to fuzzy to be meaningful. Also, Physics Forums is meant for the discussion of mainstream physics ideas. From the Physics Forums rules,

Sorry, I read your forum rules. Now understand that this is a forum for study, not ideas. Sorry to bother you, I think I will quit the account here.

 

[dendros]

Hello. I hope not bother you if you post again. I apologize again because I violated the rules of the forum. From now on, I keep ideas for me and I will refer only to GR. I read his book again Einstein, cited above, and we reached some conclusions about which I'm not sure it is correct. From what I read, that in a local reference system placed in a variable gravity field are non-inertial effects. Ie the reference system placed in the gravitational field continuously-variable physical sizes, such as the mass (energy by default), geometric dimensions, speeds (including speed of light) are also continuous-variable. I understood correctly? If so, why they say that the speed of light is a limit, since it is continuously-variable?