Trisecting an angle

[mfgoode]

:surprised
So, what happens when a body recedes at 100% of the speed of light?

infinity.

Therefore (1 + z) will be equal to infinity and so will z be equal to infinity.

No body can therefore recede at a speed equal to the speed of light. This is another way of saying that a body at the observable edge of the universe is invisible.
http://www.aqua.co.za/assa_jhb/Canopus/c999evz.htm
Mally

[cheesehead]

But, Mally, I need to add a correction to my latest posting.

The equations referenced there are valid in a flat universe with cosmological constant = 0.0, if I understand correctly. Since observations (of high-redshift supernovae) have shown that our universe doesn't satisfy those conditions, there need to be corrections to those equations.

Quoting from two other sources:

Originally Posted by http://www.astro.ucla.edu/~wright/doppler.htm

When z is larger than 1 then cz is faster than the speed of light and, while recession velocities faster than light are allowed, this approximation using cz as the recession velocity of an object is no longer valid. Thus for the largest known redshift of z=6.3, the recession velocity is not 6.3*c = 1,890,000 km/sec. It is also not the 285,254 km/sec given by the special relativistic Doppler formula 1+z = sqrt((1+v/c)/(1-v/c)). The actual recession velocity for this object depends on the cosmological parameters, but for an OmegaM=0.3 vacuum-dominated flat model the velocity is 585,611 km/sec.

(So z=6.3 corresponds to an actual recession velocity of 1.95c !)

Originally Posted by http://www.astro.ucla.edu/~wright/cosmology_faq.html#FTL

Can objects move away from us faster than the speed of light?

Again, this is a question that depends on which of the <A href="http://www.astro.ucla.edu/~wright/cosmo_02.htm#MD">many distance definitions one uses. However, if we assume that the distance of an object at time t is the distance from our position at time t to the object's position at time t measured by a set of observers moving with the expansion of the Universe, and all making their observations when they see the Universe as having age t, then the velocity (change in D per change in t) can definitely be larger than the speed of light. This is not a contradiction of special relativity because this distance is not the same as the spatial distance used in SR, and the age of the Universe is not the same as the time used in SR. In the special case of the empty Universe, where one can show the model in both special relativistic and cosmological coordinates, the velocity defined by change in cosmological distance per unit cosmic time is given by v = c ln(1+z), where z is the redshift, which clearly goes to infinity as the redshift goes to infinity, and is larger than c for z > 1.718. For the critical density Universe, this velocity is given by v = 2c[1-(1+z)-0.5] which is larger than c for z > 3 .

For the concordance model based on CMB [Cosmic Microwave Background - cheesehead] data and the acceleration of the expansion measured using supernovae, a flat Universe with Omega_M = 0.27, the velocity is greater than c for z > 1.407.

[ppo]

Do you mean that in order to trisect an angle one has to work faster than the speed of light?

[garo]

I was thinking of splitting this thread but after ppo's last post decided against it

[Wacky]

Originally Posted by garo

I was thinking of splitting this thread but after ppo's last post decided against it.

I didn't know that you had that power.

Actually, I had the same thought. I felt that most of the discussion was "off topic" and belonged in a separate thread (probably in some other part of the forum).

But ppo put us straight!

[garo]

Originally Posted by Wacky

I didn't know that you had that power.

Actually, I had the same thought. I felt that most of the discussion was "off topic" and belonged in a separate thread (probably in some other part of the forum).

But ppo put us straight!

Heh! Super-mod

Actually, I don't care very much if ppo's post manages to bring us back on topic. But the way the thread has evolved it would be a shame to split it. The sum of the two parts would certainly be less than the whole.

[mfgoode]

Originally Posted by ppo

Do you mean that in order to trisect an angle one has to work faster than the speed of light?

You don't have too! If you open a scissors fast enough (Finite speed) the point of separation of the two blades can move at the speed or greater than the speed of light (Feynman). :surprised
In the good old days we used to call it a 'virtual' velocity. Today anything 'virtual' is connected with cyber- games et al.
To reiterate a mass less object can travel faster than light speed. There is proof of the existence of tachyons which are always faster than the speed of light but never come below the speed light (c). Theoretically this is possible and compatible with both the theories of Relativity.
As a simple exercise imagine a mirror at a distance 'd' from an object. If the mirror (and not the object) is moved at even half the speed of light away from the object, the image will be moving at 'c' Over half 'C' of the mirror the image moves faster than 'c'
If you cant fathom it out ask a high school student to work it out for you
Mally

[mfgoode]

How do you add velocities in Special Relativity?
Check this out.
[URL]http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html[URL]
Mally

[xilman]

Originally Posted by mfgoode

You don't have too! If you open a scissors fast enough (Finite speed) the point of separation of the two blades can move at the speed or greater than the speed of light (Feynman). :surprised
In the good old days we used to call it a 'virtual' velocity. Today anything 'virtual' is connected with cyber- games et al.
To reiterate a mass less object can travel faster than light speed. There is proof of the existence of tachyons which are always faster than the speed of light but never come below the speed light (c). Theoretically this is possible and compatible with both the theories of Relativity.
As a simple exercise imagine a mirror at a distance 'd' from an object. If the mirror (and not the object) is moved at even half the speed of light away from the object, the image will be moving at 'c' Over half 'C' of the mirror the image moves faster than 'c'
If you cant fathom it out ask a high school student to work it out for you
Mally

True, but not very useful.

What relativity *really* says is not that things can't travel faster than light but that information can not be conveyed from place to place at faster than a constant value c. Experiment shows, to extremely high accuracy, that light travels at c in vacuo. There's nothing particularly special about light. It is not the only phenomenon with this behaviour. Physicists would be seriously worried (and very excited) if gravitational waves didn't also travel at c for instance. Pump enough energy into just about anything and you can make it travel as close to c as you wish.

None of the phenomena you give above transfer information from point to point along the path taken.

Paul

[Fusion_power]

Mally,

I have to call you on the "proof of the existence of tachyons" statement above. The last I knew of this, there was theoretical probability but no absolute proof. Do you have something that would prove your statement?

What of quantum entangled particles? Does the event propagate at the speed of light when one of the particles is destroyed? What happens to the energy imbued in an entangled particle when its mate is destroyed?

Fusion

[mfgoode]

Originally Posted by xilman

True, but not very useful.

What relativity *really* says is not that things can't travel faster than light but that information can not be conveyed from place to place at faster than a constant value c. Experiment shows, to extremely high accuracy, that light travels at c in vacuo. There's nothing particularly special about light. It is not the only phenomenon with this behaviour. Physicists would be seriously worried (and very excited) if gravitational waves didn't also travel at c for instance. Pump enough energy into just about anything and you can make it travel as close to c as you wish.

None of the phenomena you give above transfer information from point to point along the path taken.

Paul

'True but not very useful'.
Well how useful was it conquering Everest? or building the pyramids or Solomons Temple? Because its in the mind of Man and the collective consciousness. The Spirit of man will not die!

I think that 'things' more scientifically should be called mass-less objects or 'minus mass' objects/particles.

I agree that information cannot be transferred faster than c as it is maintained that the 'limiting velocity of interaction' in the universe is c.
Today c is defined by the standard meter and not the other way around.

The particularity of c is that all electromagnetic radiation travels at c. This was theorised by Faraday and Maxwell long before the Special Theory was formulated and due to this 'find' that Lorentz developed his transformation.
At the time one could very well have said 'Not very useful, so what?'

Pumping energy into mass to reach c requires an infinite quantity as the mass will tend to infinity as it approaches c using the B (beta) formula.

Still infinite forces are real as can be seen in several mechanical linkages.
The 'side rod' of a steam engine provides an infinite force for a split second and that's why journals reach metal fatigue and break.
There is every possibility that g-waves travel at c as also postulated by Einstein.
LIGO claimed that they have detected g-waves between observations some 2000 miles apart. :surprised
Mally