Acceleration..

[snoopy]

I must say to Tormod

 

Love the new Avatar...

 

Its inspired genius...

 

I Love it..

 

 

where can I get one ??

 

Peace

:D

[Pyrotex]

Hopefully I'm not putting words in Pyro's mouth (unlike nothing [inside joke])

:) :) :D :phones:

when I say:.

Every "event" conceivable is bound by the Light Cone.

If we can't see it, it didn't happen.

Spot on!

 

Here, the word "can't" means "cannot in principle" -- it is NOT a reflection on our technology or ingenuity.

 

...nothing...

:bump: :) :hihi:

[Qfwfq]

So the distant supernova didn't happen until we observed it...

[freeztar]

So the distant supernova didn't happen until we observed it...

 

I see your point Q.

I'm sure we are are all on the same page here, but clarification is always good.

 

If we think of the "beginning" of the universe (big bang, what have you), then that is the "truest" light cone. So at the "edge" of the universe, we can't see beyond, so it's safe to assume that the light cone is "expanding" into these areas of the "universe that is not there yet". (sorry for the layman speak, but I must be quick while my girl gets ready for the party tonight :D )

 

So it's not that the supernova didn't happen until we observed it. It's that once we were able to observe to such a distance, we were able to observe the distant supernova. It's light cone and ours have been in intersection for a long time, we just couldn't observe it yet.

 

"If you can't see it, it didn't happen" is not meant to be taken too literally. :doh:

[LaurieAG]

Hopefully I'm not putting words in Pyro's mouth (unlike nothing [inside joke]) when I say:.

Every "event" conceivable is bound by the Light Cone.

 

I see this light cone as mathematically inconsistent and entirely innapropriate because when you reduce it to one element (i.e. light travels in a straight line) by removing the future and the past nothing really changes.

 

It is mathematically inconsistent in that it implies that when your derivative goes past 1 (x^0 or integrated past x^-1) it goes to (x^-1 or x^1). i.e. instead of V on top of ^ you really have ^ on top of ^. The answer is always zero if you are always looking forward instead of looking both forwards and backwards at the same time.

 

I don't think that it is appropriate to use an irrational progression (that has causual inconsistencies) as an aproximation of a physical continuum and expect that calculus or any other pure mathematical function can be applied consistently.

[snoopy]

So the distant supernova didn't happen until we observed it...

 

 

Yeah light cone diagrams shouldnt be taken too literally....

 

another point I dont understand that well is why the light cone has a slope of 45 degrees, I know its connected with the Lorentz transformation but not how ?

 

Perhaps someone could clarify this for me ?

 

As always any answers appreciated

 

Peace

:)

[Erasmus00]

another point I dont understand that well is why the light cone has a slope of 45 degrees

 

In units where c = 1, the equation for the front of a propagating beam of light, sent in the x direction at t = 0 is x = t. If we plot this on a spacetime x/t diagram, it is a line, of slope 1, which means it leaves the origin at 45 degrees.

-Will

[snoopy]

In units where c = 1, the equation for the front of a propagating beam of light, sent in the x direction at t = 0 is x = t. If we plot this on a spacetime x/t diagram, it is a line, of slope 1, which means it leaves the origin at 45 degrees.

-Will

 

Hi Will,

 

How does this relate to the Lorentz transformation ?

 

What happens if space isnt Homogeneous ?

 

Peace

:)

[Erasmus00]

Hi Will,

 

How does this relate to the Lorentz transformation ?

 

What happens if space isnt Homogeneous ?

 

It doesn't relate to the Lorentz transforms, except in so far as world lines inside the lightcone will always be mapped to world lines inside the lightcone under a lorentz transformation.

-Will

[modest]

So your saying that we can ignore the effects of mass outside the visible universe?

I'm off topic because the original question has been answered.

 

Looks like Einstein was asking the same question when developing GR.

 

http://www.tc.umn.edu/~janss011/pdf%20files/Einstein-De%20Sitter.pdf

They agreed that general relativity, as it stood, preserved a remnant of Newton’s absolute space and time, since boundary conditions played a role alongside matter in determining the metric field and thereby the inertial properties of the universe. De Sitter did not find this at all objectionable, but Einstein wanted to eliminate this absolute element by postulating degenerate values for the metric field at infinity—which he thought would ensure that the inertial mass of test particles at infinity vanishes (see Einstein 1917, pp. 145–146)—and the existence of distant masses that would somehow cause these degenerate values at infinity to turn into Minkowskian values at large but finite distances. De Sitter sharply criticized this proposal. He argued that Einstein’s distant masses would have to be outside the visible part of the universe, and that an explanation of the origin of inertia invoking such invisible masses was no more satisfactory than one invoking Newton’s absolute space and time.

Einstein came to accept De Sitter’s criticism and abandoned the proposal. As he wrote to De Sitter on February 2, 1917: “I have completely abandoned my views, rightfully contested by you, on the degeneration of the g-mu-nu.

I am curious to hear what you will have to say about the somewhat crazy idea I am considering now.” In his famous paper “Cosmological Considerations on the General Theory of Relativity” ( Einstein 1917 , see Lightman 1991 , p. 16) published later that month, he circumvented the problem of boundary conditions at infinity simply by abolishing infinity! That is to say, he introduced a spatially closed model of the universe.

 

-modest

[coldcreation]

Looks like Einstein was asking the same question when developing GR.

 

http://www.tc.umn.edu/~janss011/pdf%20files/Einstein-De%20Sitter.pdf

 

 

Einstein came to accept De Sitter’s criticism and abandoned the proposal. As he wrote to De Sitter on February 2' date=' 1917: “I have completely abandoned my views, rightfully contested by you, on the degeneration of the g-mu-nu.

I am curious to hear what you will have to say about the somewhat crazy idea I am considering now.” In his famous paper “Cosmological Considerations on the General Theory of Relativity” ( Einstein 1917 , see Lightman 1991 , p. 16) published later that month, he circumvented the problem of boundary conditions at infinity simply by abolishing infinity! That is to say, he introduced a spatially closed model of the universe.[/quote']

 

Yes, but the de Sitter model that followed was (is) infinite spatiotemporally.

 

So the boundary condition was (is) still alive and kicking.

 

 

CC

[modest]

Yes, but the de Sitter model that followed was (is) infinite spatiotemporally.

 

So the boundary condition was (is) still alive and kicking.

 

CC, please describe the boundary condition you're talking about and how it relates to distant masses in de sitter spacetime

 

thank you

 

-modest

[coldcreation]

CC, please describe the boundary condition you're talking about and how it relates to distant masses in de sitter spacetime

 

thank you

 

-modest

 

Sure. In the de Sitter model, circa 1917, the ‘time-like interval’ depends on distance, meaning that clocks would appear to slow down depending on distance (the further away, the slower the clock) - manifesting itself as a redshift (the so-called de Sitter effect).

 

The relation to distant masses: depending on the interpretation of the de Sitter redshift, a particle placed in the manifold tends to accelerate (as in the Doppler effect), meaning that distant masses would be accelerated to c (in comparison with our own reference frame) at the horizon.

 

Or if the the dilution in the rate of photon arrival is not due to the stretching of the path length as a function of time, then it is due to the cosmological non-linear geometric Gaussian curvature of the 3-space metric through which light must propagate (the original de Sitter interpretation).

 

So the boundary condition, then, was located on the horizon: clocks would appear to stop (again, in comparison with our own reference frame).

 

The boundary condition now is located at the Plank time, near t = 0 (whatever that means). Physics stops there. One could say, then, that beyond that point only metaphysics remains. Whether this is a real physical problem or reflects simply a lack of knowledge about the boundary condition is up in the air (anyone's guess).

 

That's the short version...

 

 

 

CC