Theory of relativity second postulate

[Paul77]

Hi,
the theory of relativities second postulate is:-

The speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the source of the light

A physical process occurs when a photon is being emitted and this process takes place at speed of light. If you are moving towards the incoming photon one would expect the apparent speed of the photon, before allowing for your own speed, to be greater than c.

Am I right in thinking that the second postulate says that the apparent speed is still c?

I think it does - how can this be?

Thanks

 

[Bob_for_short]

c = constant is an experimental fact.

Besides, the light velocity is so high, that for our our daily motions it can be considered as infinity. One does not note its finiteness.

See http://www.univ-nancy2.fr/poincare/bhp/hp1906rpen.xml

 

[Naty1]

Hi Paul...

A physical process occurs when a photon is being emitted and this process takes place at speed of light. If you are moving towards the incoming photon one would expect the apparent speed of the photon, before allowing for your own speed, to be greater than c.

I can't make any sense of either of these statements. For example, how does one measure the speed of a physcial process (in time) relative to the speed of light (a velocity). Phrasing questions is NOT easy.

Am I right in thinking that the second postulate says that the apparent speed is still c?

Yes. Einstein took experimental findings of his day, that "ether" apparently did not exist as previously hypothesized, and took the radical step of assuming that it was the speed of light that is fixed for all observers, regardless of their velocity or the velocity of the light source.
He put this 'crazy' idea together with time length contraction (from Lorentz) and time dilation (from Fitzgerald) and voila, special relativity was born. So instead of the speed of light varying, as might seem "logical", for observers at at high speed it is space and time that change while the speed of light remains fixed!

If you think the constant speed of light is "odd", "strange" or "counterintuitive", which it of course is, wait until you get into quantum mechanics...now there's "weirdness"!

 

[Bob_for_short]

...it is space and time that change while the speed of light remains fixed!

No, it is lengths of bodies and clock readings that change, not the space and time themselves. In space there are many flying bodies with different velocities. According to which velocity the space should contract?

 

[Dale]

No, it is lengths of bodies and clock readings that change, not the space and time themselves.

Please don't go down this pointless discussion yet again. You don't strike me as a crackpot with an agenda, but this argument is a crackpot argument.

 

[Bob_for_short]

Please don't go down this pointless discussion yet again. You don't strike me as a crackpot with an agenda, but this argument is a crackpot argument.

Could you translate it into the plain English for me, please? (What is "a crackpot with an agenda"?)

 

[Paul77]

Re: "A physical process occurs when a photon is being emitted and this process takes place at speed of light."

What I mean't here was that a photon is traveling at the speed of light towards the observer (by some process).

Re: "If you are moving towards the incoming photon one would expect the apparent speed of the photon, before allowing for your own speed, to be greater than c"

If we were talking about a car traveling towards you at a velocity of 100m/s and you were traveling towards it at 50m/s it looks like the oncoming car is traveling at 150m/s until you allow for your own speed. So if you were traveling towards a source of light at, for arguements sake, half the speed of light, the apparent speed of the photon coming at you would be one and a half times the speed of light.

So is the second postulate saying that the photon's apparent speed, before allowing for your own speed, is always equal to the speed of light?

Re: the Micholson Morley aether experiment - I'm not sure this helps - as it just demonstrates there is no aether 'following wind' in any direction.

 

[Janus]

No, it is lengths of bodies and clock readings that change, not the space and time themselves. In space there are many flying bodies with different velocities. According to which velocity the space should contract?

According to which inertial frame the space is being measured from.

If you have two points in space that are 1 light year apart in their own rest frame:

To a frame traveling at 0.866 c parallel to the line joining these two points, the space between them contracts to .5 ly. To a frame traveling in the same direction at 0.99 c, it will contract to 0.141 ly.

Do not fall into the trap of thinking of time and space as rigid frameworks against which the action of clocks and the length of objects are judged.

 

[Bob_for_short]

If you have two points in space that are 1 light year apart in their own rest frame:

Indeed, it does not look as a solid body.

To a frame traveling at 0.866 c parallel to the line joining these two points, the space between them contracts to .5 ly. To a frame traveling in the same direction at 0.99 c, it will contract to 0.141 ly.

You see, your way of "length" measurement depends on the frame velocity. And I can make measurements that will give the proper length (space-like interval). This is another way of distance measurements. And being a wise man, I choose the latter way of the space arithmetization. So the space in my RF is a set of still points, not moving ones.

In addition, when we study a relativistic particle motion r(t), we never speak of continuous distance |r| contraction due to varying velocity vector v(t). At least me, - I never heard of that.

On the other hand, if we study a physical rod, it makes sense to speak of its length contraction since in some experiments it looks as contracted.

_______________________________
"Me know much, me understand little."

 

[Dale]

Could you translate it into the plain English for me, please? (What is "a crackpot with an agenda"?)

A crackpot with an agenda is someone with an anti-science (usually anti-relativity) bias that seeks to promote their own poorly-formed theory with no experimental justification and usually little understanding of the scientific method, math, or experimental facts. I don't believe you are such a person, but your above statement is typical of them.

 

[HallsofIvy]

Hi,
the theory of relativities second postulate is:-

The speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the source of the light

A physical process occurs when a photon is being emitted and this process takes place at speed of light. If you are moving towards the incoming photon one would expect the apparent speed of the photon, before allowing for your own speed, to be greater than c.

Am I right in thinking that the second postulate says that the apparent speed is still c?

I think it does - how can this be?

Thanks

Yes, it does. The formula for combining speeds, in relativity, is
$$\frac{u+ v}{1+ uv/c^2}$$
That is, if you are moving toward point A at speed u, relative to some observer, and another object is moving toward point A from the opposite direction with speed v, relative to that same observer, then the object is moving toward you with speed, relative to you, of
$$\frac{u+v}{1+ uv/c^2}$$, not u+ v.

In particular if that "object" is light, so that v= c relative to the observer, then its speed, relative to you, is
$$\frac{u+c}{1+ uc/c^2}= \frac{u+c}{1+ u/c}= \frac{c(u+c)}{c+u}= c$$
So light has speed c relative to any frame.

If u and v are on the order of "ordinary speeds", much less than the speed of light, the combined speed is still less than u+ v but 1+ uv/c² is so close to 1 that the difference is unmeasurable.

 

[Paul77]

Its true following your formula through for objects moving at c whatever the other's velocity, u, we get c as the result. But its still just a formulae - how did someone come up with this formulae??

 

[JesseM]

Its true following your formula through for objects moving at c whatever the other's velocity, u, we get c as the result. But its still just a formulae - how did someone come up with this formulae??

It's derived from the Lorentz transformation relating the coordinates of different inertial frames to each other, which itself is derived from the two fundamental postulates of SR. If one frame assigns coordinates x,t to an event, and there is another frame whose spatial origin is moving along the first frame's x-axis at speed v (with the spatial origins of each frame coinciding at t=0 and t'=0), then the Lorentz transformation says that the same event will have the following x',t' coordinates in the second frame:

x' = gamma*(x - vt)
t' = gamma*(t - vx/c^2)
with gamma = 1/sqrt(1 - v^2/c^2)

If you like I can show how to derive the velocity transformation equation from this, or give you some links on how the Lorentz transformation is derived from the two fundamental postulates.

 

[sangeetulhas]

i think its c.can anyone tell me if any particle can travel at the speed of light?i heard that particles can only travel at speed more than or less than the speed of light and that if they travel at the speed of light , it will be transformed to energy.

 

[Paul77]

Thanks for the info on the Lorentz transformation - I'm still looking at the derivation
(http://www.bartleby.com/173/a1.html) - if you have another that's any easier
please post the link. From what I can see the maths on adding the speeds of two inertial frames leads to equations which are hyperbolic. And this is the reason that there is a finite limit on how fast things can travel even if there was no limit on the process employed.

I think this limit then necessarily leads to the 'creation' of gravity since spacetime
is no longer fixed.

If gravity is a 'side-effect' of this limit why do we need a quantum explanation of gravity?
Does'nt the maths of inertial frames equally apply to the movement sub-atomic particles and so isn't time and space oscilating with the interaction and movement of these particles and these oscilations will be summed as you zoom out from the microscopic to the large scale.

 

[Paul77]

When I said sub-atomic I meant atomic and molecular - ie isn't gravity the sum of the
movement of these particles - so why do we need a quantum theory of gravity?

 

[JesseM]

Thanks for the info on the Lorentz transformation - I'm still looking at the derivation
(http://www.bartleby.com/173/a1.html) - if you have another that's any easier
please post the link.

You can find various derivations online if you google the words Lorentz transformation derivation, if anyone here has any favorites, please post them...I posted my own mini-derivation in post 14 of this thread although I don't think it's very rigorous.

I think this limit then necessarily leads to the 'creation' of gravity since spacetime
is no longer fixed.

I don't think so, how do you figure? In general relativity gravity involves curvature of space time, whereas the Lorentz transformation just deals with different inertial coordinate systems in the "flat" uncurved Minkowski spacetime of SR. It seems perfectly possible to imagine a hypothetical universe where SR holds exactly, and Lorentz-symmetric laws like Maxwell's laws of electromagnetism or the laws of quantum field theory still apply, but where mass and energy don't give rise to spacetime curvature and thus there is no gravitational force.

 

[Paul77]

I don't think so, how do you figure? In general relativity gravity involves curvature of space time, whereas the Lorentz transformation just deals with different inertial coordinate systems in the "flat" uncurved Minkowski spacetime of SR.

Does'nt everything go back to the hyperbolic nature of the Lorentz transformations.
Its due to this that, even mass-less photon's traveling in a vacuum, are limited to their maximum speed and from that things that were fixed, space and time, are no longer.

The curvature of time and space is merely the next step in a chain of consequences when you apply this limitation in a wider context.

It seems perfectly possible to imagine a hypothetical universe where SR holds exactly, and Lorentz-symmetric laws like Maxwell's laws of electromagnetism or the laws of quantum field theory still apply, but where mass and energy don't give rise to spacetime curvature and thus there is no gravitational force.

My impression was that special relativity is a special case - a reduced model - dealing with inertial coordinate systems and that relativity theory is a jump from a phenonemon of spacetime being malable to spacetime formed into depressions (in which the planets and the sun sit).

You seem to imply that there is more to this and that gravity is not a natural extension of the limit on speed that you need something else before mass and energy can warp spacetime - can you expand?