Galilean relativity and acceleration

In summary, the conversation discusses the concept of the equivalence principle in general relativity, which states that free-fall in a gravitational field is equivalent to floating freely in the absence of gravity. This means that gravity is not a force, but rather a result of curved space-time caused by massive objects. The conversation also mentions the idea of a sudden appearance of a star and how it would affect an observer in a closed box, with the conclusion that it would result in a tidal force rather than a feeling of acceleration. The conversation also clarifies that while the equivalence principle applies in both Newtonian gravity and general relativity, the latter allows for any coordinate transformation to be equivalent to a gravitational field. Lastly, the conversation mentions the issue of energy conservation in
  • #1
AndyVo
3
0
Hello all. I'm a long time reader and a first time poster. I should start by saying that I am not a physicists or a physics student and am studying it merely out of curiosity so please forgive any ambiguous terms I may use that are not standard.

I came up with a sort of thought experiment to do with classical or special relativity. It is my understanding that to an observer in a closed environment such as a train there is no experiment that can betray uniform velocity. However acceleration can be detected. This makes intuitive sense when we think about how it feels to travel in an actual train.

But consider an observer in a closed box in outer space. Say that all of a sudden a star were to manifest itself from nothing some distance from this box. Suddenly there will be a force imparted on this box from the gravity of the star and it will be accelerated towards the star.

Is there anyway to detect this occurrence? That is, does the has the box's inertial frame of reference change? Intuitively it seems that this isn't detectable since everything inside the box is being accelerated at the same rate. (Doesn't free fall feel the same as 0 gravity?) Yet relativity states that acceleration is detectable.

I'm pretty certain my confusion stems from a fundamental misunderstanding of relativity but I'm not sure where I've gone wrong. Any help would be greatly appreciated.
 
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  • #2
In General Relativity, a freely falling object is equivalent to an object moving with a constant velocity in flat space-time. Both are considered inertial.

In your sealed box, you wouldn't be able to tell the difference between falling toward a star and moving with a constant velocity in flat space-time.

Relative to the star, the falling object is accelerating but it isn't proper acceleration. If you had an accelerometer while freely falling, it would read zero. In contrast, standing on the surface of the earth, you are rest relative to the ground but your instrument would measure an acceleration of 9.8m/s2- the latter scenario being equivalent to being on a ship in flat space-time firing its rockets and accelerating.

In GR, gravity isn't a force and objects aren't really attracted to each other; they are merely following curved paths (geodesics) through space-time. The curvature of space-time is caused by massive objects.

Wikipedia said:
In general relativity, a geodesic generalizes the notion of a "straight line" to curved space-time.

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

One caveat: If the object is large enough, or is falling toward a very massive object- a black hole for example, tidal forces become significant and the equivalence between the two scenarios break.

Tidal forces still exist for a small object falling toward the Earth or the sun, but are so small they can be ignored.

Here are a couple lectures that may help:

 
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  • #3
AndyVo said:
Is there anyway to detect this occurrence? That is, does the has the box's inertial frame of reference change? Intuitively it seems that this isn't detectable since everything inside the box is being accelerated at the same rate. (Doesn't free fall feel the same as 0 gravity?) Yet relativity states that acceleration is detectable.

I'm pretty certain my confusion stems from a fundamental misunderstanding of relativity but I'm not sure where I've gone wrong. Any help would be greatly appreciated.

You're doing just fine here, as this is the basic insight that led Einstein to realize that free-fall in a gravitational field is no different than floating free in the absence of any gravity - they're both inertial frames. In general relativity, gravity isn't a force and it doesn't produce acceleration.

Search this forum and the net for "equivalence principle" for more details.
 
  • #4
All right. Thanks for the quick and informative replies. It's starting to make a bit more sense. I'll look up the "equivalence principle" for more information :).
 
  • #5
AndyVo said:
...Say that all of a sudden a star were to manifest itself from nothing some distance from this box. Suddenly there will be a force imparted on this box from the gravity of the star and it will be accelerated towards the star.

Is there anyway to detect this occurrence?...
You're proposing a gravitational tsunami. What the physicists wouldn't give for such an occurrence. They're building very delicate instruments to detect extremely small gravity waves. Of course you would be able to detect the gravity from the sudden creation of new mass. But don't worry, it's not going to happen.
 
  • #6
Say that all of a sudden a star were to manifest itself from nothing some distance from this box.

Actually, you WOULD experience a force, a tidal force squeezing you together. Kind of like someone walking up behind you and pushing your shoulders together. Your free fall acceleration wouldn't be detected for the reasons outlined by the other commentators, but depending on the density and distance of this "presto" star, you would feel that tidal effect more or less. If that star were a black hole not so far away, that pushing on your shoulders would soon spaghettify you in a way that the force was certainly felt.
 
  • #7
Haha yes that makes sense. So you would feel it but not in the sense that you feel you are accelerating. Interesting stuff, for me at least since it's all fairly new.
 
  • #8
The equivalence principle also holds in Newtonian gravity. There, any time-dependent acceleration can be rewritten as a gravitational field. The big difference with GR is that in GR any coordinate transformation is equivalent to some gravitational field. So e.g., in Newtonian gravity an observer with a time-dependent rotation cannot pretend he/she is in a gravitational field, while in GR this would be possible (locally).
 
  • #9
AndyVo said:
Say that all of a sudden a star were to manifest itself from nothing some distance from this box.

Strictly speaking, this can't happen: it would violate energy conservation. But you could imagine the closed box starting out far away from all other objects, but happening to have a trajectory that will take it close to a star. The effect would be basically the same, and everything the other posters have said would still apply.
 
  • #10
AndyVo said:
Hello all. I'm a long time reader and a first time poster. I should start by saying that I am not a physicists or a physics student and am studying it merely out of curiosity so please forgive any ambiguous terms I may use that are not standard.

I came up with a sort of thought experiment to do with classical or special relativity. It is my understanding that to an observer in a closed environment such as a train there is no experiment that can betray uniform velocity. However acceleration can be detected. This makes intuitive sense when we think about how it feels to travel in an actual train.

But consider an observer in a closed box in outer space. Say that all of a sudden a star were to manifest itself from nothing some distance from this box. Suddenly there will be a force imparted on this box from the gravity of the star and it will be accelerated towards the star.

Is there anyway to detect this occurrence? That is, does the has the box's inertial frame of reference change? Intuitively it seems that this isn't detectable since everything inside the box is being accelerated at the same rate. (Doesn't free fall feel the same as 0 gravity?) Yet relativity states that acceleration is detectable.

I'm pretty certain my confusion stems from a fundamental misunderstanding of relativity but I'm not sure where I've gone wrong. Any help would be greatly appreciated.
In addition to the other responses, you will of course be able to detect that you are falling towards that star if you look out of the window; the box is not anymore approximately an inertial frame (in the usual sense of "Galilean" reference system). :smile:

Also a disambiguation: in post #3 "inertial frame" includes gravitation with inertia - thus a "free-fall-frame".
 
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  • #11
harrylin said:
In addition to the other responses, you will of course be able to detect that you are falling towards that star if you look out of the window; the box is not anymore approximately an inertial frame (in the usual sense of "Galilean" reference system)..

The one thing that makes the box not an inertial frame if you look far enough outside it is the tidal forces. In the absence of rotation of the box, the presence of tidal forces is both necessary and sufficient to show that you're not in an inertial frame. (With a sophisticated enough definition of tidal force you might be able to eliminate the remark about the box rotating, but if you just naively look for differences in acceleration on two ends of a rigid bar, you could conceiviable mislabel rotation of the box as a tidal force.)

"Looking out the window" just gives you a more sensitive way to measure the tidal force - a tidal force that has little effect over the cramped inside of the box might be much more obvious when integrated over a longer distance.

So I'd say that "looking out the window" doesn't really tell you all that much, it's mostly just a matter of even a small tidal force becoming noticeable if you integrate it over a long enough distance.

To present the formal argument, the presence of a true tidal force shows that there is geodesic deviation, and the geodesic deviation demonstrates that there is a non-zero curvature tensor, which means GR.
 
  • #12
pervect said:
The one thing that makes the box not an inertial frame if you look far enough outside it is the tidal forces. [..] "Looking out the window" just gives you a more sensitive way to measure the tidal force [..]
I meant "looking" literal: surely optical effects can show it (aberration? Doppler? ..)
 
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  • #13
Why are we talking about a window in the box? The whole idea of the box is to prevent you from seeing or looking outside of it. It's not suppose to be a structure that you make measurements from. You're supposed to imagine that you are freely floating inside the box which is what will happen in reality.
 

1. What is Galilean relativity?

Galilean relativity is a principle of classical mechanics stating that the laws of motion remain the same for all observers moving at constant velocities. It is named after the Italian scientist, Galileo Galilei, who first proposed this concept in the 16th century.

2. How does Galilean relativity differ from Einstein's theory of relativity?

Galilean relativity only applies to objects moving at constant velocities in straight lines, while Einstein's theory of relativity applies to all types of motion, including those at high speeds or in gravitational fields. Additionally, Einstein's theory takes into account the concept of spacetime, while Galilean relativity does not.

3. What is meant by "acceleration" in Galilean relativity?

In Galilean relativity, acceleration refers to a change in velocity over time. It can be described as the rate at which an object's speed or direction of motion changes.

4. How does Galilean relativity explain the behavior of objects in free fall?

According to Galilean relativity, objects in free fall will accelerate due to the force of gravity acting on them. This acceleration will be the same for all objects, regardless of their mass, as long as they are in the same gravitational field.

5. What are some real-world applications of Galilean relativity?

Galilean relativity is commonly used in everyday applications, such as predicting the motion of objects in projectile motion or understanding the behavior of vehicles in motion. It is also essential in the design and functioning of many modern technologies, such as airplanes, cars, and satellites.

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