Confusions over general relitivity

[Paper]

I have a few questions:
1. From what I understand, light always travels at C, no matter what medium it is in. If it encounters matter, it can be absorbed and retransmitted, giving the illusion that it has traveled slower, but in actual fact, when it has traveled it has propagated at C. Is this correct?

2. As time and space can be considered in terms of dimensions, it can be thought that light traveling in "space-time" travels along a spatial dimension and also "along" time. I understand that since the velocity is fixed, the two things that change relative to a viewer sitting still are time and distance. What I don't understand is how they change and how Einstein managed to come to the conclusions he did without being able to test out his theories?

3. I understand that as the velocity of an object increases, so does it's mass, due to E=mc^2. However I'm not sure if this is really actually mass, as we might think of it every day, or merely that at this level of physics, we must abandon the traditional notion of mass? Again how did Einstein come to the conclusion of E=mc^2?

4. I understand that gravity is not a force as Newtonian physics states and instead mass "bends" space-time towards itself so that an object seemingly traveling in a straight line follows the curvature of space-time. Thus objects are "encouraged" towards the mass. Am I right?

5. I don't really understand what makes an object move through space towards another mass, simply because that other mass has bent space. If the mass was not moving but you held it above earth, surely it would move towards the Earth even with no deliberate energy been given to it. Where does the energy come from to accelerate the object?

6. And finally, is this bending of space-time only applicable to rest mass? If not, then surely as light has energy, it also had a mass that affects space-time?

Thanks

 

[Fredrik]

1. Yes.

2. It's more accurate to say that motion is represented by curves in spacetime. However, this isn't what distinguishes relativity from pre-relativistic physics. The difference is that in SR we have to distinguish between coordinate time and proper time in non-relativistic physics. (See post #21 here). This is what makes simultaneity "relative" in SR.

Also, don't forget that some aspects of special relativity had already been tested before Einstein: Maxwell's equations had been around for a while, and they are consistent with SR but not with pre-relativistic spacetime.

3. Physicsts prefer to let the word "mass" mean "rest mass". The other kind of mass, "relativistic mass", is a concept that isn't very useful. You only need it to understand older texts. The full equation is E^2=m^2c^4+\vec p^2c^2. E=mc² is the special case of zero momentum. Alternatively, it can be interpreted by rewriting the equation as E^2=m_0^2c^4+\vec p^2c^2=m^2c^4 and taking the right-hand side to be the definition of "relativistic mass".

I don't know how he found it, but one way to find it is to calculate the work required to accelerate a massive particle from speed 0 to speed v. See e.g. #15 here (and skip the first paragraph).

4. It's of course more complicated than that, but you've got the right idea. The motion of a free particle is still represented by a "straight" curve in spacetime, but the presence of mass changes the geometry so that another set of curves are considered "straight". Such curves are called "geodesics".

5. In GR, a falling object isn't accelerating. Acceleration is a deviation from geodesic motion. An object resting on the surface of the Earth is accelerating, pushed by the normal force from the ground which prevents it from doing geodesic motion.

6. There are ten independent quantities that affect the geometry of spacetime (look up "stress-energy tensor"), and one of them is mass/energy.

 

[A.T.]

5. I don't really understand what makes an object move through space towards another mass, simply because that other mass has bent space.

It doesn't bend just space but space-time. If you try to move straight in a curved space-time, your direction in regard to the dimensions changes (geodesic deviation). And your direction in space-time determines your movement in space. It is easier to understand it with pictures. Try the ones linked here:
https://www.physicsforums.com/showpost.php?p=2244927&postcount=21

If the mass was not moving but you held it above earth, surely it would move towards the Earth even with no deliberate energy been given to it. Where does the energy come from to accelerate the object?

The object has potential energy due to its position a gravitational field. Just like in Newtons Gravity.

 

[Paper]

Thank you for your replies, but I think I'm a bit more confused...

In question 2 I was really asking how time dilation and spatial contraction work, in simple terms you'd use for a school child. From what I get, time and distance must change, relative to someone else not travelling, in order to accommodate a constant speed.

Also, for light, https://www.physicsforums.com/latex_images/22/2270065-1.png would imply that the p^(-2)c^2 is significant, as the rest mass m0 is always zero. So therefore if I get it right, p, the momentum, is proportional to the energy of the light? Thus, different frequencies produce different momentums?

I'm a bit confused about geodesic motion. It's to say that an apple dropped above the Earth speeds up towards the Earth at an increasingly constant rate, yet has no acceleration? And that this apple is simply compelled to move because the geometry of space has been warped? Yet as a gravitational force doesn't exist, there is no force being exerted on the apple?

What is the nature of geodesic motion? Is it that this motion is simply inherent to all things in the universe? It seems rather Aristotelian to me, things moving towards a "natural" position.

I can understand the idea of gravitational potential - it's a bit like a spring that stretches, but gets easier to stretch the more you do so, rather than harder?

So in number 6, light does warp space-time?

I remember learning this at school, but I never understood it then. I always have wondered why the language used to describe physics is so complex. Glancing at the first few results that come up in google for "stress-energy tensor", and yet still I have no idea what it means. Why is there this obsession in science for using words that generally don't make sense?!

 

[A.T.]

I'm a bit confused about geodesic motion. It's to say that an apple dropped above the Earth speeds up towards the Earth at an increasingly constant rate, yet has no acceleration?

It has no absolute acceleration (proper acceleration), that an accelerometer would measure. Depeneding on the frame of reference it can have some coordinate acceleration (dv/dt).

And that this apple is simply compelled to move because the geometry of space has been warped?

Again: space-time not space. Warped space alone would not affect an object at rest in space, which the apple initially is.

Yet as a gravitational force doesn't exist, there is no force being exerted on the apple?

Yes, that's why the apple experiences no proper acceleration.

What is the nature of geodesic motion?

Take some sticky tape and stick it to a curved surface like a vase, without folding and tearing it. It follows a geodesic, because it actually is a straight line, when you unroll it onto a flat surface.

Is it that this motion is simply inherent to all things in the universe? It seems rather Aristotelian to me, things moving towards a "natural" position.

Not all things, just the free falling ones. No net force acting -> geodesic advance in space time. Just like in classical Newtonian mechanics, but the space-time can be curved now.

Why is there this obsession in science for using words that generally don't make sense?!

Science provides definitions for all words it uses, which explain their sense.

 

[Fredrik]

Also, for light, https://www.physicsforums.com/latex_images/22/2270065-1.png would imply that the p^(-2)c^2 is significant, as the rest mass m0 is always zero. So therefore if I get it right, p, the momentum, is proportional to the energy of the light? Thus, different frequencies produce different momentums?

Yes, this is right.

I'm a bit confused about geodesic motion. It's to say that an apple dropped above the Earth speeds up towards the Earth at an increasingly constant rate, yet has no acceleration? And that this apple is simply compelled to move because the geometry of space has been warped? Yet as a gravitational force doesn't exist, there is no force being exerted on the apple?

What is the nature of geodesic motion? Is it that this motion is simply inherent to all things in the universe? It seems rather Aristotelian to me, things moving towards a "natural" position.

Think of it this way instead: Any definition of acceleration must tell us which objects are not accelerating. In all the theories of space, time and motion (Newtonian, SR, GR), motion is represented by curves in spacetime, so we have to specify a set of curves and then define "inertial motion" by saying that anything that moves as described by one of those curves is doing inertial motion. We could of course pick a coordinate system more or less at random and then say that the curves that have a constant velocity in those coordinates are to be thought of as not accelerating. But this isn't very consistent with the principle of relativity, and if we choose this option we certainly won't be able to build "accelerometers" that can distinguish between "inertial" and "non-inertial" motion. The only way to give us any chance of doing that successfully is to choose a set of curves that have some coordinate independent property, and "being a geodesic" is such a property. It's the only coordinate independent property that makes any sense to use for this purpose.

Note that to "pick a coordinate system more or less at random" is precisely what you did. You picked one in which the surface of the Earth is stationary. In such a coordinate system, it's true that a falling apple "speeds up", but you can easily define another coordinate system in which it's slowing down instead. Your apple is accelerating, not because of the physics, but because you chose to use a coordinate system in which it's accelerating.

If we define "inertial motion" to be "geodesic motion", as discussed above, then we can define "proper acceleration" as a measure of the deviation from geodesic motion.

Glancing at the first few results that come up in google for "stress-energy tensor", and yet still I have no idea what it means.

No one said that it would be easy.

Why is there this obsession in science for using words that generally don't make sense?!

What A.T. said. Also, can you think of a better word for it? Maybe something like "momentum flow tensor field" would be better, but that wouldn't make it any easier for you to learn what it is.

 

[Paper]

Ah thank you both of you. It's getting a bit clearer. Oh and usually when I say space, I mean space-time (although I don't know whether it's considered acceptable to shorten it as such). I understand now that the object indeed does not accelerate in geodesic space-time, because the coordinate system for geodesic space means that it merely has a constant velocity. Do I get it right? Anyway, I'll keep reading :)

When I was criticising the word usage for not making sense, I didn't mean the title given to things. I meant the descriptions we get given, especially at school, e.g. "Blaa blaa is a vector quantity within a four dimensional geo...etc". Such descriptions, IMO, don't help you grasp the concepts in your mind's eye, something which is done by comparison or example. So (ironically, an example to show what I mean) instead of the wikipedia definition of gravity:
"In everyday life, gravitation is most commonly thought of as the agency which lends weight to objects with mass. Gravitation compels dispersed matter to coalesce, thus it accounts for the very existence of the Earth, the Sun, and most of the macroscopic objects in the universe."

I would say: "In everyday life, gravity is an interaction, classically a force, between all mass (from objects right down to individual atoms), causing each and every bit of mass to come together. When people say "weight", scientifically they mean their mass, which is measured in kilograms. But scientific weight is a force mass exerts (e.g. on a table) due to gravity ("the heaviness") and it's measured in Newtons. Gravity accounts for the very existence of the Earth, the solar system and the universe."

See, is this not easier to understand? Ok it's in baby language, but it says exactly the same thing as the complicated sentence.

 

[A.T.]

Oh and usually when I say space, I mean space-time (although I don't know whether it's considered acceptable to shorten it as such).

This is the main source of misconceptions about gravity in GR, which finds its expression in bad analogies like the rubber-sheet with the bowling ball. You will not get it until you get this difference.

I understand now that the object indeed does not accelerate in geodesic space-time, because the coordinate system for geodesic space means that it merely has a constant velocity. Do I get it right?

Not really, you just introduced the terms "geodesic space" and "geodesic space-time", which are not useful here. Try not to make stuff more complicated than it is: Acceleration means advancing in space-time on a non-geodesic path. Look a the links I gave you.

 

[Paper]

Well I tried. I dunno, all these numbers and examples with lines don't make sense to me. I think I aught to go back to youtube, so I can watch, pause, process, watch and etc... What a complicated theory - but I'm sure there is a better way to put it than the way it is stated it now!

 

[A.T.]

Well I tried. I dunno, all these numbers and examples with lines don't make sense to me.

If you don't get diagrams, you will have a hard time understanding a geometric theory.

What a complicated theory - but I'm sure there is a better way to put it than the way it is stated it now!

It won't get simpler than that: http://www.physics.ucla.edu/demoweb...alence_and_general_relativity/curved_time.gif
Falling object advances straight ahead trough curved space-time, and therefore starts moving in space.

 

[DaveC426913]

I think I aught to go back to youtube...

Or read a book...