Light

Recommended Posts

5 hours ago, geordief said:

a bit out of my comprehension zone, but just to clarify  you are talking about a possible external  gravitational and/or em  field?

Yes, I am talking, in this particular case, about an external EM field. What Tim88 posted assumes such a field. length contraction is not related to this.

Share on other sites

26 minutes ago, bvr said:

Yes, of course, in the moving frame the observed equilibrium will be different (and in fact the same as that of the object when it was at rest in the original frame).

If they are the same, how can they be different?

Share on other sites

2 hours ago, swansont said:

If they are the same, how can they be different?

In the original frame, where the object was at rest at the beginning, there was a certain equilibrium on it's structure. When it was brought into movement, it's structure changed and came to a different equilibrium.

In the co-moving frame, where the object stays at rest, it's structure didn't change and the observed equilibrium is still the same as that observed in the original frame when the object was at rest, and different from the new observed equilibrium in the original frame.

Share on other sites

45 minutes ago, bvr said:

In the original frame, where the object was at rest at the beginning, there was a certain equilibrium on it's structure. When it was brought into movement, it's structure changed and came to a different equilibrium.

In the co-moving frame, where the object stays at rest, it's structure didn't change and the observed equilibrium is still the same as that observed in the original frame when the object was at rest, and different from the new observed equilibrium in the original frame.

You seem to be assuming a "mechanistic" cause for Relativistic effects. This is not how Relativity deals with them.  As I stated above, Relativity is about the geometry of Space-time.  As an analogy, imagine that you have a 4 ft long board and a 3 ft wide doorway. The board won't fit through the door cross-wise, but if you rotate it some, you change its effective "width"with respect to the door's width and it will it fit through.  You haven't altered the "structure" of the board in any way, you just changed its orientation with respect to the door.   In Relativity, relative motion changes the relative orientation in space-time between frames. Objects moving relative to you undergo length contraction because you are measuring its length from a different space-time "angle" than it measures its own length.  And since this angle difference is in space-time, it also causes you to measure clocks traveling on that object to run slowly and a disagreement over simultaneity between the two frames.

Share on other sites

On ‎03‎/‎08‎/‎2017 at 6:02 PM, geordief said:

thanks.Hopefully that will sink in after a while.

Perhaps the train guard will hammer it home for you.

Share on other sites

1 minute ago, studiot said:

Perhaps the train guard will hammer it home for you.

we are mixing metaphors .I am still waiting for the plumber   to put the sink in.

Share on other sites

Quote

BVR said

On ‎04‎/‎08‎/‎2017 at 10:23 AM, studiot said:
On ‎04‎/‎08‎/‎2017 at 9:04 AM, bvr said:

There are no more (or less) forces acting when an object is moving. It's an equilibrium. Of course there was once another force involved, the acceleration.

Isn't the underlined part a contradiction in terms?

I don't see a contradiction. I'm speaking of the equilibrium of the internal structure of the object.

On ‎04‎/‎08‎/‎2017 at 10:23 AM, studiot said:

In fact isn't equilibrium another one of those characteristics that depend on the observer in einstinian relativity?

Yes, of course, in the moving frame the observed equilibrium will be different (and in fact the same as that of the object when it was at rest in the original frame).

On ‎04‎/‎08‎/‎2017 at 10:23 AM, studiot said:

And when you refer to 'forces', do you mean Newtonian forces or four-forces?

I mean the forces which hold the atoms together in an object.

I think you misunderstand both my comments and mechanics.

Forces are forces whether they are internal or4 externally applied.

A rigid body maintains its shape, not because the forces are internal, but because every particle of that body is subject to the same accelerating force.

But it may be that no particle of that body is in equilibrium.

Fast forward to Einstein.

I asked if when you refer to forces you are referring to Newtonian or four- forces.

Why does in make any difference if they are internal?

To obtain a vector equation to balance (make equal to zero) all the vectors must be of the same type.

So they must be all Newtonian vectors or Minkowskian vectors.

Share on other sites

Ah good ole vectors, There is a very neat trick to understanding SR and GR inherent in understanding vector calculus. That trick is to understand the differences between the dot product and the cross product of two vectors. This is also important to understand Lorentz boosts and rotations. All boosts use the dot product.  All rotations use the cross product. This includes the hyperbolic trigonometric functions. Its also coincidentally the key to understanding the following.

1) orthogonality, when orthogonality of all planes of axis is preserved use Euclid trigonometry (at rest frame) Galilean relativity rules apply

2) acceleration=rapidity=rotation

3) righthand rule=covariant=lefthand=contravariant. (accleration and conservation of angular momentum) =rotational translations

4) kronecker delta is a dot product

5) Levi Cevita connection is a cross product.

6) principle of equivalence is a dot product

though the knowing all dot products are scalars ie the dot product of two vectors is a scalar and the cross product of the same two vectors is a vector. Is of critical importance to understand the above aforementioned.

here is a good look at cross product, the links on that page will get you to the dot product section.

its a handy site as it details the above in matrix form, however one must look at the specifics of the Lorentz boosts and rotations to with regard to relativity but the 3d dot product and cross product rules do apply in 4d but one has to study the commutations on the 4*4 matrixes. (the above is a preliminary before you step into 4d).

The above naturally also applies to div and curl....flux, pressure,vorticity etc

now an easy way to visualize hyperbolic trigonometry as per polar coordinates, take a rubber sheet draw a triangle upon said sheet. Write all all your trig functions that correspond to this sheet with the dot product rules.

then take the sheet and fold it over a sphere, the vectors that make up the triangle are now curved not linear, so you now have different lengths on each vector. (cross product of hyperbolic trig functions, via the addition of a curvature term k.).

In Lorentz the curvature term only applies to the ct,x coordinates. via the gamma factor Lorentz boost. The zeroth component is e=pc^2 your invariant speed of light.

Now here is a neat trick to the above the Minkowskii metric preserves the inner dot product which when preserved also preserves orthogonality. However that is the MInkowskii tensor itself, when you undergo translations this will return a scalar value. examples, mass,energy, velocity, frequency, temperature, etc any scalar quantity. We do not need to add any dimensions to the dot product.

However cross products such as angular momentum adds a vector perpendicular to vectors a and b so you need an additional dimension or degree of freedom. or dimension.

PS note the matrix designations on the 3*3 matrix for cross product and dot products. All dot products (scalar values lie on the diagonal components.) this includes scalar value 0 as per conservation laws

these curves are all hyperbolic.

You can see the Hyperbolic vectors in this Kruskal diagram

notice the curl of $\phi$ ?

Now with the above, and as per the first image we can use the parallel transport of two vectors to determine our curvature. (in freefall under GR).

The two vectors will converge on the center of mass giving loss of parallel transport,

Edited by Mordred
Share on other sites

Now that's what I call a proper answer from someone who knows (a lot) more than I do about the subject and its details.

Thanks Mordred +1

Share on other sites

edit had to double check the boosts,  which can be thought of as a rotation between space and time.  will correct the above. Corrected I knew there was something I had to be careful on when we hit the 4d lol

Edited by Mordred
Share on other sites

30 minutes ago, Mordred said:

edit had to double check the boosts,  which can be thought of as a rotation between space and time.  will correct the above. Corrected I knew there was something I had to be careful on when we hit the 4d lol

I was under the impression that vector products of vectors was peculiar to 3D and for 4D you had to go to quaternions or the equivalent tensors

Share on other sites

The mistake I had was  boosts as a scalar which is obviously wrong. A boost is a matrix so what you stated applies its the three vector that has the perdindicular component.

That was what I almost forgot

Edited by Mordred
Share on other sites

On 8/5/2017 at 5:41 PM, Janus said:

You seem to be assuming a "mechanistic" cause for Relativistic effects. This is not how Relativity deals with them.  As I stated above, Relativity is about the geometry of Space-time.

Yes, for you as a physicist, that's obvious.
But you won't succeed to explain the relativistic effects that way to laymen.
So, what's wrong with the mechanistic view? Of course it's incomplete (a complete description would be very complicated and involve QM) and approximative (but your analogy of the geometric description is so too).
But I don't think it's contradictory, nor exclusive, to the geometric description, and it can give an idea of what's going on in a way that is comprehensible for everyone.
Even for teaching Relativity on undergraduate level a constructive approach can be prefered at the beginning, see Miller A constructive approach to the special theory of relativity .

Share on other sites

On 05/08/2017 at 2:15 PM, swansont said:

Yes, I am talking, in this particular case, about an external EM field. What Tim88 posted assumes such a field. length contraction is not related to this.

That's probably the same misunderstanding: what I quoted from Bell was about length contraction (the Lorentz-Fitzgerald kind) related to internal EM fields. That's part of a more "constructive" approach to teaching SR.
PS: that is exactly what bvr meant with the remark that you claimed to be wrong, as we see just now in his latest post.

If you think that you can disprove Bell's "How to teach relativity" then please start it as a new topic, so as not to hijack the discussion here about understanding light propagation in SR. It would certainly deserve a discussion thread on its own, and it can be interesting.

Edited by Tim88
typo, phrasing
Share on other sites

1 hour ago, Tim88 said:

That's probably the same misunderstanding: what I quoted from Bell was about length contraction (the Lorentz-Fitzgerald kind) related to internal EM fields. That's part of a more "constructive" approach to teaching SR.
PS: that is exactly what bvr meant with the remark that you claimed to be wrong, as we see just now in his latest post.

If you think that you can disprove Bell's "How to teach relativity" then please start it as a new topic, so as not to hijack the discussion here about understanding light propagation in SR. It would certainly deserve a discussion thread on its own, and it can be interesting.

The internal force argument is, IMO, problematic, but you are correct, that's for another thread. But that was not the only statement of bvr's which I objected to. The clock analysis — that the timing changes because of the distance between atoms (which allegedly increases?) — is bogus. The simplest rebuttal is that you can have a clock that's a single atom or ion. Or a linear ion trap, situated in the vertical direction. There is no length contraction effect, and yet the time will follow relativity.

Share on other sites

1 hour ago, swansont said:

[..] that was not the only statement of bvr's which I objected to. The clock analysis — that the timing changes because of the distance between atoms (which allegedly increases?) — is bogus. The simplest rebuttal is that you can have a clock that's a single atom or ion. Or a linear ion trap, situated in the vertical direction. There is no length contraction effect, and yet the time will follow relativity.

From my side I also have some difficulties with posts by different people, for example I can guess what bvr may have meant with "measuring light with light", but I'm not sure. Probably it's an oversimplification; remember the intended level of this thread. I hope that he'll clarify that as geordief already asked for.

Concerning time dilation, the simplest illustration is the light clock - which is a very nice illustration of time dilation at a beginners level and appropriate for this discussion. It illustrates something similar as what bvr may have had in mind (again simplifying). As determined in the "rest" frame, the light clock's "time" is indeed "dilated" because the signal trajectories between "moving" atoms (mirrors in this case) are increased. That's the first stepping stone towards understanding the Michelson-Morley experiment. It may be useful for geordief to have a look at it.
- https://simple.wikipedia.org/wiki/Light_clock
- https://en.wikipedia.org/wiki/Time_dilation#Simple_inference_of_velocity_time_dilation
(not sure that "simple wikipedia" is the easiest to understand)

Edited by Tim88
Share on other sites

"measuring light with light" was indeed an oversimplification, even a pun (probably not the best idea for a clear explanation).
I just wanted to indicate the similarity of propagation of light and of all other electromagnetic phenomena.

A light clock is indeed the simplest illustration of time dilation.
If we accept that a light clock physically slows due to increased light path:

we should admit that "something analogue" happens in any co-moving clock, if both continue to tick at the same rate.

Share on other sites

15 hours ago, bvr said:

"measuring light with light" was indeed an oversimplification, even a pun (probably not the best idea for a clear explanation).
I just wanted to indicate the similarity of propagation of light and of all other electromagnetic phenomena.

A light clock is indeed the simplest illustration of time dilation.
If we accept that a light clock physically slows due to increased light path:

we should admit that "something analogue" happens in any co-moving clock, if both continue to tick at the same rate.

Of course we admit that the effect happens in any co-moving clock. But you proposed a specific mechanism, which is an incorrect extrapolation of the light clock explanation.

Create an account

Register a new account