Can One Grasp Relativity Without Doing the Math?

[Ziggurat]

No (by definition more or less), but I can give you two metrics for the same matter configuration, which is more to the point.

I don't think it is. If a given metric only has one mass/energy configuration which satisfies it, then I think that's all you need in order to distinguish between gravity and acceleration.

Not a pure acceleration metric, no. I'm talking about cases where there is some of "both".

OK then, can you give me two different mass/energy and acceleration combinations which produce the same metric?

 

[sol invictus]

I don't think it is. If a given metric only has one mass/energy configuration which satisfies it, then I think that's all you need in order to distinguish between gravity and acceleration.

The problem is you can't tell whether the mass/energy configurations are the same.

Look: take some given metric and compute the stress-energy tensor, which let's suppose is non-zero and relatively complex. Now apply some nasty non-linear coordinate transformation to the metric. Those two metrics of course represent the same physical spacetime. But the forces as measured by a set of observers at rest in the two will be very different, and if you compute the stress-energy tensor of the second, it can look very very different from that of the first.

Mathematically the problem is determining whether two spacetime metrics are related by a coordinate transform. AFAIK that's an unsolved problem. Physically the problem is separating "inertial" forces from "true" gravitational ones. I don't believe such a distinction really exists.

 

[Vorpal]

Just to be clear, are you arguing about whether in a coordinate frame it is possible in general to distinguish the effects of gravity and the effects of acceleration of that frame?

I almost agree with you, Sol, but I don't understand your given reason. Specifically, I don't understand how a positive resolution of the metric equivalency problem (for spacetimes) would conceptually change the situation. Suppose you had an oracle that told you whether two metrics are related by a coordinate transformation, and the transformation itself. Maybe it's even nice enough to automatically find geodesics for you and make other coordinate frames that follow them.

Even with all of these difficulties hypothetically melted away, what would it mean to "separate" the effects of gravity and acceleration in that coordinate frame? Are we looking at, say, the geodesic equation and saying these terms are this, those terms are that, etc.? That does make sense in some cases (flat spacetime being the simplest, of course--e.g., a rotating frame has very obvious centrifugal/Coriolis force terms), but I'm a bit confused how I would go about this in general even I had a magic box that divined coordinate transformations on demand.

 

[Tumbleweed]

I just finished a Great Course 24 lecture CD called Einstein's Relativity and the quantum revolution, Modern Physics for non scientists and it made it quite clear why you cannot go faster than the speed of light: Because the laws of physics INCLUDING those regarding electromagnetic radiation MUST work the same in each frame of reference. So if I can throw a ball on the ground so can somebody on a jet plane with the EXACT same physics at work regarding that tossed ball for both of us, assuming constant relative velocities. And if I determine that light is ALWAYS traveling away from me at c regardless of my speed, then by God it has to be the same for everybody in every other frame of reference, just like tossing the ball is. Light goes away at c from EVERYBODY no matter what their relative velociites are. Increase your speed an the light waves propagated a minute ago are STILL going away from you at c. How can you catch them if they are ALWAYS going c no matter WHAT the hell you do. And by the way, the professor (Wolfson) started out the course by flatly declaring that the 1% of scientists who imagine things through thought experiments are far far more important than the 99% that just crunch the numbers in equations

 

[sol invictus]

Just to be clear, are you arguing about whether in a coordinate frame it is possible in general to distinguish the effects of gravity and the effects of acceleration of that frame?

Yes.

I almost agree with you, Sol, but I don't understand your given reason. Specifically, I don't understand how a positive resolution of the metric equivalency problem (for spacetimes) would conceptually change the situation. Suppose you had an oracle that told you whether two metrics are related by a coordinate transformation, and the transformation itself. Maybe it's even nice enough to automatically find geodesics for you and make other coordinate frames that follow them.

Even with all of these difficulties hypothetically melted away, what would it mean to "separate" the effects of gravity and acceleration in that coordinate frame? Are we looking at, say, the geodesic equation and saying these terms are this, those terms are that, etc.? That does make sense in some cases (flat spacetime being the simplest, of course--e.g., a rotating frame has very obvious centrifugal/Coriolis force terms), but I'm a bit confused how I would go about this in general even I had a magic box that divined coordinate transformations on demand.

I think we're in agreement. There are two separate questions at issue here:

a) can two metrics (or two sets of physical measurements) be used to determine whether or not the two spacetimes in question are in fact identical up to a coordinate transform. At the moment, the answer to that is "no" in general, "yes" in special cases.

b) given a particular spacetime in some coordinates, can we distinguish "gravity" from "acceleration"?

Here's a suggestion (based on a few second's thought) for how to try to answer b) in the affirmative. It requires slightly more than the metric: given a metric and the value of G, compute the Einstein tensor and equate it to the stress-energy times 8piG. Now consider the one-parameter family of metrics related to the first one by solving Einstein's equations for the same stress-energy tensor but with different values of G (the parameter). Consider the limit G->0. Any forces that remain in that limit are to be considered inertial forces. The "difference" between that set of forces and those at finite G are gravitational.

The problem with this definition is taking the "difference", since the metrics are different as well. Still, perhaps one could make something of that at least in some weak-field limit.

 

[Tumbleweed]

I must say this gravity thing confuses me. If as Einstein states it is a geometrical manifestation, then why are they looking for a particle as the cause of space deformation? Can't it simply be the moving mass itself that is distorting space and time?

 

[Beerina]

1. Gravity and acceleration aren't just similar phenomena -- they're exactly the same phenomenon

2. You are traveling through 4-dimensional spacetime (3 space and 1 time dimension, like frames in a movie) at the speed of light. This is always constant, relative to you. This seems odd because you don't feel you are moving. And you aren't, through the 3 space dimensions. You are therefore moving through time, "forward", at the speed of light.

3. If you change your speed through space, you must therefore also change your speed through time so the total speed remains the speed of light. This is why the faster you go, relative to other things, your speed through time varies, relative to other people's speed through time. To them, your speed through space is now non-zero, and therefore, to them, your speed through time must slow, relative to them.

Hence the "astronaut" who goes away at high speed and then returns finds himself much younger than his twin brother he left behind on Earth.

4. Gravity is a warpage in this 4-dimensional spacetime. Since it's warped, your "speed" through 3-space (relative to the gravity source) is not zero. Since your total speed (relative to you) through spacetime must remain the speed of light, something gives, and that has to be movement through time, which therefore slows to compensate.

You feel gravity because you are literally accelerating through this warped 4-dimensional spacetime just to "stay in the same place", which is to say, to maintain your speed through it at the speed of light.





Did I miss anything? That's my interpretation, the key points being 1 and 2. They aren't just descriptions that happen to work, but are the way reality "actually is".

 

[martu]

I must say this gravity thing confuses me. If as Einstein states it is a geometrical manifestation, then why are they looking for a particle as the cause of space deformation? Can't it simply be the moving mass itself that is distorting space and time?

I can't help you (sorry!) but I have a question about this too, when it is written that space is distorted what is 'space'? We have ruled out an ether so how can one say there is a shape at all?

 

[Raze]

I can't help you (sorry!) but I have a question about this too, when it is written that space is distorted what is 'space'? We have ruled out an ether so how can one say there is a shape at all?

I'm pretty sure that the "ether" we "ruled out" was defined as a medium required for light to propagate through, and which provided a special reference frame in which Maxwell's equations were correct (instead of, "Maxwell's equations are laws of nature" it was "Maxwell's equations describe how electromagnetic phenomena behaves in the preferred reference frame which is at rest with respect to the ether, or some such stuff...).

So I'd say it isn't quite the same thing. But I am vastly ignorant about relativity, so don't take my word for it.

 

[sol invictus]

I must say this gravity thing confuses me. If as Einstein states it is a geometrical manifestation, then why are they looking for a particle as the cause of space deformation?

Because geometry is composed of particles, or so it seems.

1. Gravity and acceleration aren't just similar phenomena -- they're exactly the same phenomenon
<snip>
4. Gravity is a warpage in this 4-dimensional spacetime.
<snip>
Did I miss anything? That's my interpretation, the key points being 1 and 2. They aren't just descriptions that happen to work, but are the way reality "actually is".

Problem - one can feel inertial forces due to acceleration in spacetimes that are completely flat and unwarped, at least if "warped" means non-zero spacetime curvature.

I can't help you (sorry!) but I have a question about this too, when it is written that space is distorted what is 'space'? We have ruled out an ether so how can one say there is a shape at all?

The truth seems to lie somewhere between the 19th century idea that space was full of a fluid, ether, and the idea that space has no characteristics at all. According to Einstein's theories, space does have certain physical properties. For example there's an absolute "rest" frame for acceleration. Another example is that one can excite propagating ripples of spacetime by moving mass and energy around.

 

[phildonnia]

You just have to figure out the following two facts:
1) The laws of nature appear the same, no matter how fast you're moving
2) The constant speed of light is a law of nature
Some people need math to wrap your head around this. I suppose there are other ways of seeing the light.

#1 is probably easier to appreciate today than it was in the early 20th century, since more people have had the experience of traveling smoothly at high speeds and noticing that everything feels and behaves normally.

 

[ponderingturtle]

You just have to figure out the following two facts:
1) The laws of nature appear the same, no matter how fast you're moving
2) The constant speed of light is a law of nature
Some people need math to wrap your head around this. I suppose there are other ways of seeing the light.

#1 is probably easier to appreciate today than it was in the early 20th century, since more people have had the experience of traveling smoothly at high speeds and noticing that everything feels and behaves normally.

1) is not quite right, it is really "as long there is no acceleration the laws of physics are the same for all observers and they will all observe the same events.

 

[Brian-M]

I must say this gravity thing confuses me. If as Einstein states it is a geometrical manifestation, then why are they looking for a particle as the cause of space deformation? Can't it simply be the moving mass itself that is distorting space and time?

Its because relativity is incompatible with quantum theory, and neither theory provides a complete explanation for everything on it's own. I think they're searching for gravity particles in order to test a quantum theory of gravity, not the relativity theory of gravity.

I vaguely recall a plan to put lasers on three orbiting satellites in order to test whether or not space is warped by the earth's mass. If space is being warped, the angles formed by the triangle of lasers connecting these satellites won't add up to exactly 180 degrees. I have no idea if this experiment is actually going to be done.

 

[Raze]

1) is not quite right, it is really "as long there is no acceleration the laws of physics are the same for all observers and they will all observe the same events.

I thought general relativity expanded that postulate to all frames, whether inertial or not inertial, with accelerations and gravitational fields being pretty much the same. ??? (hence the "general" in the phrase "general relativity," I had thought).

Of course, I am a novice, so... :shrugs:

 

[ponderingturtle]

I thought general relativity expanded that postulate to all frames, whether inertial or not inertial, with accelerations and gravitational fields being pretty much the same. ??? (hence the "general" in the phrase "general relativity," I had thought).

Of course, I am a novice, so... :shrugs:

I am not that farmiliar with GR but I don't think it is still a universal. Take the example of a spinning reference frame. The guy on the merry go round will see different effects when he bounces a ball no matter how smooth the merry go rounds motion is. This can be accounted for sure but that does not mean that they are the same.

 

[Raze]

I am not that farmiliar with GR but I don't think it is still a universal. Take the example of a spinning reference frame. The guy on the merry go round will see different effects when he bounces a ball no matter how smooth the merry go rounds motion is. This can be accounted for sure but that does not mean that they are the same.

No, I don't mean that they will observe the same thing, but that the laws of physics will be the same for both, adding in the postulate that a gravitational field is indistinguishable from a uniform acceleration. i.e. the guy on the spinning frame is in a gravitational field, and that is what accounts for the ball not following Newton's laws.

 

[Raze]

Also ponderingturtle,

http://en.wikipedia.org/wiki/Principle_of_relativity#General_principle_of_relativity

There it says that the general principle of relativity says:

" All systems of reference are equivalent with respect to the formulation of the fundamental laws of physics.

That is, physical laws are the same in all reference frames -- inertial or non-inertial."


And then it talks about Einstein devising the whole "acceleration is gravitation thing."



Any more knowledgeable people want to explain to us?

 

[sol invictus]

Also ponderingturtle,

http://en.wikipedia.org/wiki/Principle_of_relativity#General_principle_of_relativity

There it says that the general principle of relativity says:

" All systems of reference are equivalent with respect to the formulation of the fundamental laws of physics.

That is, physical laws are the same in all reference frames -- inertial or non-inertial."


And then it talks about Einstein devising the whole "acceleration is gravitation thing."



Any more knowledgeable people want to explain to us?

That wiki is extraordinarily badly written.

What Einstein actually showed is how to formulate the laws of physics in a way that allows one to write them in any coordinate system (i.e. reference frame), including non-inertial ones. They retain the same overall form, but the laws themselves are certainly not the same.

For example, F=ma is invalid in a non-inertial frame (if "F" means external forces). You must add extra terms - so-called "fictitious forces" - to that equation to make it valid. However Einstein showed there is a way to re-write that law so that it does look the same in all frames, basically by using a set of symbols that transform nicely when you change frames and automatically include all the relevant fictitious forces.

 

[Marduk]

I aint grasping none of my relatives

 

[ponderingturtle]

No, I don't mean that they will observe the same thing, but that the laws of physics will be the same for both, adding in the postulate that a gravitational field is indistinguishable from a uniform acceleration. i.e. the guy on the spinning frame is in a gravitational field, and that is what accounts for the ball not following Newton's laws.

Um, not at all. An accelerating field is the same as a gravitational field a rotating field is much more complex. See Coriolis forces.

You can work out the equations sure, if you know in what way your reference frame is non inertial, but the general form of the equations do hold.

I am not convinced that in an accelerating reference frame momentum would be conserved for example.