What are the implication of Einstein's definition of space time?

[ArielGenesis]

I know the answer is many, some of them I already understand very well, time dilation etc, some other I might be able to grasp the idea (like light cone) and I will not be able to understand some others (i can't name it because i don't know what i don't know)

I am a 2nd year physics major, just scratch the surface of SR and given a little peek hole by my lecturer about GR. I think before I go to my 3rd year, it is a good idea to be able to think in relativistic term intuitively before I jump into all the formula and equation and calculation that will be thrown at me at my later years.


1. lorent'z transformation are defined in term of speed of light and speed if light itself is determined in terms of epsilon and mu. In the case of non-vacum, light travel slower, and thus the slower version of speed of light is then subtituted for the lorentz's transformation? does the permiability and permifity of free space changes the space-time nature of the space it self?

2. a number of things travel at the speed of light, one of them is, of course, light. other things are the composition of lights, such as magnetic and electric field, and also gravitational field. (or changes in those field I should say). Is asking why these things travel in the speed of light is a valid question? is it because these information carry no mass (does not bend spacetime) or it is just the nature of these things? or is it because the nature of space time?

3. if something move faster, it gets heavier, i know the precise definition is not exactly that. my question is: does this relativistic mass (not the rest mass) bend space time? and if they don't, why does the rest mass does but the relativistic mass does not?

4. I think no body knows yet but I am not sure, why does the gravitational mass and the inertial mass the same?

5. in simple geometrical/topological term, what does it exactly meant for space time to be bent? I have seen a lot of picture and I do have an idea of it but not much enough that I can intuitively built up the formalism from scratch.

Thank you.

 

[Joans]

for 1 question light always travels at same speed, it do not slow down in other objects. "Photons excite the adjoining particles that in turn transfer the energy to the neighbor. This may appear to slow the beam down through its trajectory in realtime. The time lost between entry and exit accounts to the displacement of energy through the substance between each particle that is excited." but still speed of photon is the same - c.

for 2 question as I heared from quantum physics information travels instanteniously.

for 3 energy and mass is equivalence, so where should be the same effect

for 4 question you came dow to Newtonian mechanics because inertial mass is m=F/a, and gravitation is as a force, that's because gravitation and inertial mass is the same in Newtonian mechanics, I think..

Not full answers from me, but still something. :)

 

[Dale]

I will try to answer the individual questions, but I think that the most important implications of spacetime is the unification of the various concepts that were once thought to be independent. For example, space and time, energy and momentum, electric and magnetic fields, etc.

1. lorent'z transformation are defined in term of speed of light and speed if light itself is determined in terms of epsilon and mu. In the case of non-vacum, light travel slower, and thus the slower version of speed of light is then subtituted for the lorentz's transformation? does the permiability and permifity of free space changes the space-time nature of the space it self?

It seems like you are asking which is more fundamental, the speed of light or the permeability and permittivity of free space. If so, the real answer is that only the dimensionless universal constants are truly fundamental. So the speed of light and the permeability and permittivity of free space all depend on fundamental things like the fine structure constant.

2. a number of things travel at the speed of light, one of them is, of course, light. other things are the composition of lights, such as magnetic and electric field, and also gravitational field. (or changes in those field I should say). Is asking why these things travel in the speed of light is a valid question? is it because these information carry no mass (does not bend spacetime) or it is just the nature of these things? or is it because the nature of space time?

If something is massless but carries energy and momentum then it must move at c in all reference frames.

3. if something move faster, it gets heavier, i know the precise definition is not exactly that. my question is: does this relativistic mass (not the rest mass) bend space time? and if they don't, why does the rest mass does but the relativistic mass does not?

In GR the source of gravity is not just mass, it is the stress-energy tensor which has 10 independent terms, only one of which is the relativistic mass. As you increase the relativistic mass you also increase one or more of those other terms which affects the gravity in a complicated way. The bottom line is that you cannot take a solution for a static spacetime (like the Schwarzschild solution which predicts black holes) and apply it to a non-static spacetime (like a relativistically moving planet).

4. I think no body knows yet but I am not sure, why does the gravitational mass and the inertial mass the same?

Science is inherently unable to answer the fundamental why questions. But the equivalence between inertial mass and gravitational mass is the basis of the equivalence principle and the geometrical view of gravity in GR.

5. in simple geometrical/topological term, what does it exactly meant for space time to be bent? I have seen a lot of picture and I do have an idea of it but not much enough that I can intuitively built up the formalism from scratch.

It mostly means that "straight" lines that were parallel at one spot in spacetime may intersect each other. This is important because the motion of a free particle (no forces) is a straight line, if spacetime were not bent then two initially parallel worldlines (objects at rest wrt each other) could never intersect each other without bending as they are observed to do gravitationally.

 

[Naty1]

The implications of Einstein's definition of space and time are revolutionary, one of the great paradigm shifts in physics.

For one thing, it showed the "consensus science" of the time, that space and time are fixed and immutable, was valid only for the simplist of physics. It also showed that new insights usually require new ways of thinking about things. Sure, sometimes math solutions happen to open up new unexpected avenues by "accident", like the beginnings of string theory, but it's conceptual insights, hunches, which can be confirmed by mathematical formulations which offers the real breakthroughs, especially if experimentally verifiable.

And of course Einsteins insights showed that most things are "relative", dependent on your frame of reference. For example, fall into a black hole and quantum jitters are harmless;remain suspended outside the black hole and you'll be cooked like a steak. Even simultaneity is relative. And the "barn door" paradox. And if this isn't crazy enough, within the Schwarsczshild solution for GR, space and time can swap with each other!

Things are not usually what they appear to be, and this was further illustrated by quantum mechanics which Einstein helped found, but tended to disbelieve. He also disbelieved his own mathematical work within relativity because he thought the "universe" was in a steady state; hence he introduced the cosmological constant instead of accepting the universe as explained by his own mathematics.

And don't let anyone tell you physics (and science in general) doesn't take hard work: Einstein took about ten years, from roughly age 16 to 26 to develop special relativity and another ten years after that for general relativity.

 

[ArielGenesis]

I slowly began to understand that physics take hard work the hard way, and its hard.

thanks for the reply everyone

1. "fine structure constant" never heard of that, yet. And when I said different value of permittivity and permeability, I was thinking about glass and water but I have a hunch that even in the absent of these things, those values might change.

2. I know that QM assumes that and it is definitely wrong due to the causal principle. I also have an objection, do you mean that if an 'information' carries no mass, momentum nor energy, then it could travel faster than c? Accroding to my knowledge, gravitational wave moves in the speed of light. does it carry momentum?

3. yea I think both of you kind of answer my question. Just trying to make sure that they are the same thing.

4. when I asked why what I really meant was: what is the fundamental concept that shows that these two things are in fact always equal. And the Newtonian's mechanic is simply a proof that they are. I heard of higgs boson but if nobody knows yet, then it's ok.

5. When you said that do you mean that what is locally a straight line on a, let's say, sphere, is actually a curve and light or mass will travel along the geodesic instead of 'straight' line. I do understand that doing that means something similar to measuring curved trajectories on map as the shortest distance. What I do not understand is, if I have a 'straight' ruler, and i put it on a curved space, wouldn't my ruler be bent and it will measure the correct geodesic distance anyway?

and yes, its true, I do not understand how does space and time, energy and momentum, electric and magnetic fields, gravity (now i can add fine structure constant) combine together.

the fact that we acually can swap space with time make more sense to me then if it cannot actually.

thank you

 

[Joans]

Physics is not hard, it may look complex until you do not understand it, but when you got the point it is really easy.

1. Imagine ferrari speeding throu highway(vacuum), and suddenly it come to obstacles(IN glass), but car can't slow down, because it is problem with brakes(moves always constant speed). So car must avoid all obstacles, so it moves not strait but in curves so it takes more time to travel throu that area. Imagination is very great and strong thing in physics. :) But in fact it is as I said "Photons excite the adjoining particles that in turn transfer the energy to the neighbor."

2. when i was talking about information I had in my mind about Quantum Entanglement theory..
Yep it should carry momentum (E*E=p*p*c*c+m0*m0*c*c => (m0=0) E=pc), and energy is called gravitational radiation.

I hope my little underestanding somehow helped to you

 

[Dale]

1. "fine structure constant" never heard of that, yet. And when I said different value of permittivity and permeability, I was thinking about glass and water but I have a hunch that even in the absent of these things, those values might change.

Here is a FAQ about http://math.ucr.edu/home/baez/constants.html" that I like.

do you mean that if an 'information' carries no mass, momentum nor energy, then it could travel faster than c? Accroding to my knowledge, gravitational wave moves in the speed of light. does it carry momentum?

No, if it had no mass, no momentum, and no energy then it would not exist. There is no evidence for tachyons (particles moving faster than c) but they would have negative or imaginary mass (I can't remember which). Yes, gravitons would carry momentum.

4. when I asked why what I really meant was: what is the fundamental concept that shows that these two things are in fact always equal. And the Newtonian's mechanic is simply a proof that they are.

The fundamental concept is the equivalence principle. It is the basis of GR, but I would call it a postulate rather than a proof.

What I do not understand is, if I have a 'straight' ruler, and i put it on a curved space, wouldn't my ruler be bent and it will measure the correct geodesic distance anyway?

Yes, the distance will be correctly measured. But again, the correct distance between two geodesics changes even if they are initially parallel. This is not true in flat geometry.

 

[atyy]

1. lorent'z transformation are defined in term of speed of light and speed if light itself is determined in terms of epsilon and mu. In the case of non-vacum, light travel slower, and thus the slower version of speed of light is then subtituted for the lorentz's transformation? does the permiability and permifity of free space changes the space-time nature of the space it self?

From the point of view of light "travelling through materials", the permittivity/permeability are functions of the wavelength of light, whereas in free space the are the same for all wavelengths. This change in dispersion relation changes the nature of "space and time" in materials. But from a more fundamental viewpoint, light does not really travel through materials, it interacts with the atoms etc, and the laws governing atoms light and atoms all obey special relativity.

2. a number of things travel at the speed of light, one of them is, of course, light. other things are the composition of lights, such as magnetic and electric field, and also gravitational field. (or changes in those field I should say). Is asking why these things travel in the speed of light is a valid question? is it because these information carry no mass (does not bend spacetime) or it is just the nature of these things? or is it because the nature of space time?

It's just the nature of these things, but both have in common that they are massless.

3. if something move faster, it gets heavier, i know the precise definition is not exactly that. my question is: does this relativistic mass (not the rest mass) bend space time? and if they don't, why does the rest mass does but the relativistic mass does not?

Relativistic mass bends spacetime. More generally, the stress-energy-momentum tensor bends spacetime.

4. I think no body knows yet but I am not sure, why does the gravitational mass and the inertial mass the same?

We don't know. In Einstein's theory, this is modeled as all objects following "straight lines" (geodesics) in curved space. It turns out Newtonian gravity can also be formulated in this fashion as Newton-Cartan theory.

5. in simple geometrical/topological term, what does it exactly meant for space time to be bent? I have seen a lot of picture and I do have an idea of it but not much enough that I can intuitively built up the formalism from scratch.

In special relativity, the properties of spacetime are encoded in the spacetime metric, which does not change no matter what matter is present. In general relativity, the presence of matter affects the spacetime metric.

 

[ArielGenesis]

1. I think I understand this one quiet well by now

2. when I said gravity wave, I wasn't talking about graviton, sorry for not clearing this up, I was talking about gravitational radiation such as caused by distant binary star systems.

3. I think this is clear to me by now that he answer is yes but not that simple.

4. As I supposed, this is true and no body knows why yet.

5. "The mass tells the space how to curve, and the space(-time curvature) tells the mass how to move." I know that basically summarize it but I cannot yet imagine bending time.

So if I have 2 points, A and B, on a flat fabric, the distance d will stay constant. but If due to curvature in the time axis, the would-be parallel worldline will intersect?