Absolute HOTNESS!!

[Mise]

Well the limit would have to be the sum total energy of the universe concentrated into a single point, and given entropy, a particulat point in time.

That was already answered ^^
http://en.wikipedia.org/wiki/Planck_temperature

 

[Souron]

Well the limit would have to be the sum total energy of the universe concentrated into a single point, and given entropy, a particulat point in time.

If you want an answer you want to speak to people who talk more about Planck and termodynamics, and less about the speed of light.

And for absolute zero, apply the same equation, but wait until entropy has brought about the heat death of the universe.

Yeah, there is that. The temperature of the univerce at the big bang.

btw- the univerce is infinate, so you can't concentate it all in a point.

 

[Mise]

This is technically true. The average speed of light in a vacum.

This is because of the uncertainty principle. With light, just as with any other particle, you cannot know both the position and velocity (speed and direction) at the same time.
If you were to amit a photon, according to classical (non-quantum) theory, you would know it's possition (you just amited it), speed (c) and direction of mation (a strait line away from the source). The Uncertaity principle states that those assumptions are wrong. Light does not travel in strait lines or at a constant speed.

Of course the rule is that it has to average out to traveling in a strait line at the speed of c. This is because there is equal probability that the light would go a little under the speed of light as there is that is would go a little over. And equal proabability to going a little left of a little right. Thus classically, we can think of light going in strait lines at a constant speed.

This has nothing to do with the color of light. Although as mentioned by someone earlier, different colors do travel at different speeds through different mediums.

Is this "average" speed thing referring to the difference between the group and the phase velocities?

 

[JoeM]

btw- the univerce is infinate, so you can't concentate it all in a point.

Oh right, you solved that little conundrum as well did you?

 

[Souron]

no, nothing to do with color of frequency.

It's just that there is an uncertainty in the speed of anything, light included.

It can be explained that the path a particle takes to get from point A to point B, can be anything, even if that requires going faster than light or backwards in time.

 

[Souron]

Oh right, you solved that little conundrum as well did you?

The rate the univerce is expanding is increasing. That means that the curvature is nagative. That means the univerce is saddle shaped at every point. Such a shape is infinate.

Now it is possible that this is a local phenominon; that only the local univerce is expanding progressively faster. But that defys a standard assumption that allows us to conclude that the univece is expanding in the first place: the earth is not in any special sector of the univerce (such as the center).

 

[Mise]

@Souron: The uncertainty is in position and momentum, not velocity.

 

[El_Machinae]

How can you measure velocity without knowing position?

 

[Mise]

How can you measure velocity without knowing position?

Well, you do know it's position, just not to arbitrary precision. And really we're using momentum, which in most interactions can be determined analytically (i.e. you know the momentum of the incident particle, because you gave it that momentum, and you use momentum conservation for the resulting particles after an interaction).

 

[brennan]

Sauron: since photons move at a constant velocity of c, you can say that time is meaningless to them (infinitely dilated) so while their velocity is always known, their position is fundamentally uncertain. Look at it this way: if you are a photon, the universe is infinitely small, since you can travel anywhere in zero time, so your position is always infinitely uncertain, while your momentum is known.

 

[Bill3000]

How can you measure velocity without knowing position?

It is because of the relation L = h/p, where L is the wavelength of a particle-wave. It turns out that the uncertaincy principle can be considered purely a wave phenomenon - if you have a perfect wavelength, (and thus perfectly known momentum) the wave is a sine wave; however, as a result, the amplitude (related to the probability of finding it at a position) will be completely uncertain. (Free particle equation is Y(x) = exp(i*(w*t-k*x)) - absolute square of this is 1; absolute square of the wavefunction is the probability density - this is constant, so the probability of finding it at any point will be equal to any other point) Meanwhile, if you bunch the wave up into a wavepacket, the position is more certain, but you don't have a well defined wavelength. (It would be a superposition of wavelengths) As a result, you get the uncertaincy principle. And it is completely independent of classical intuition - it's a result of the math.

Regarding the speed of light: Waves have two velocities; phase velocity and group velocity. Phase velocity is defined as w/k, where w is the angular velocity (2*pi*frequency) and k is the wavenumber (2*pi/wavelength). Group velocity is defined as dw/dk, (actually, a partial derivative) which may be different from the phase velocity. Information travels through the group velocity, not the phase velocity. The phase velocity may be larger than c (as can happen in some materials with a index of refraction > 1) but the information in the light itself travels at a speed less than or equal to c.

And regarding "prove it" and "it's just a theory" - Um, all of modern physics is based on relativity. We have our proof from modern physics at things going at relativistic speeds, which include equations that only make sense if the speed of light is a "maximum speed" (That's not actually one of the postulates of SR, only a derivation, but it works nonetheless)

As for a variable speed of light - that's pseudoscience, sorry. It's been debunked.

 

[Souron]

Sauron: since photons move at a constant velocity of c, you can say that time is meaningless to them (infinitely dilated) so while their velocity is always known, their position is fundamentally uncertain. Look at it this way: if you are a photon, the universe is infinitely small, since you can travel anywhere in zero time, so your position is always infinitely uncertain, while your momentum is known.

if that were true, then we would never be able to detect a photon. Since we can detect photons, then the velocity is not constant. Which is exatly why c is the avegage speed of light in a vacum.

 

[Souron]

@Souron: The uncertainty is in position and momentum, not velocity.

Thanks for the correction.

But what I said still holds true, because the two are closely related.

As for a variable speed of light - that's pseudoscience, sorry. It's been debunked.

Feyman diagrams clearly show particles going faster than light. And that's well accepted theory.

Read my posts, you'll see where I'm comming from.

 

[col]

Temperature is poroportional to the energy of the particle. As the particle approaches the speed of light, although it cant go any faster its mass increases so its kinetic energy ( half em vee squared) increases. There is no theoretical limit to the amount of energy a particle can have so there is no upper limit to temperature

 

[Mise]

Thanks for the correction.

But what I said still holds true, because the two are closely related.

Not for photons - the momentum of a photon is h-bar k, nothing to do with the velocity of the photon.

It may be true for massive particles, where momentum is mass x velocity, but photons have no mass.

 

[El_Machinae]

Temperature is poroportional to the energy of the particle. As the particle approaches the speed of light, although it cant go any faster its mass increases so its kinetic energy ( half em vee squared) increases. There is no theoretical limit to the amount of energy a particle can have so there is no upper limit to temperature

How does your statement jive with the concept of the Planck temperature?

 

[Fifty]

ARG! Some smart sciencey types say yes, some smart sciency types say no!

Who to believe!??!!!?!?!??!?!?!??!

I'm crying my eyes out right now


EDIT: OMG! Its even worse now. It seems the wiki article on the planck temperature cites a NIST value, and we all know that NIST tables are NOT TO BE TRUSTED. Now I just have no idea what to believe!

 

[Bill3000]

Feyman diagrams clearly show particles going faster than light. And that's well accepted theory.

Read my posts, you'll see where I'm comming from.

I do know that; however, that's not what I meant by a variable speed of light. What I mean by a "variable speed of light" is the hypothesis that the universal speed of light as a whole changes over time. I understand what you are coming from, but that isn't what I'm talking about. What I am talking about is this:

A variable speed of light cosmology has been proposed independently by John Moffat and the two-man team of Andreas Albrecht and João Magueijo to explain the horizon problem of cosmology.[20][21][22] [23] [24] [25] [26] The idea is that light propogated as much as sixty times faster in the distant past, and thus distant regions of the expanding universe have had time to interact since the beginning of the universe. As such, it was proposed as an alternative to cosmic inflation, although it is less clear how it reproduces the other successes of inflationary cosmology such as the monopole and flatness problems and how it reproduces the observed homogeneity and isotropy of the universe, and the scale invariance of the spectrum of initial perturbations.

There is no known way to solve the horizon problem with variation of the fine-structure constant, because its variation does not change the causal structure of spacetime. To do so would require modifying gravity by varying Newton's constant or redefining special relativity. (See equivalence principle for further details.) Varying speed of light cosmologies propose to circumvent this by varying the dimensionful quantity c by breaking the Lorentz invariance of Einstein's theories of general and special relativity in a particular way.[27] However, it has been pointed out by Ellis and Uzan[28] that the VSL cosmology is an ad hoc modification of various equations of physics without a consistent underlying scheme, such as a Lagrangian from which the equations of motion can be derived. It has been suggested out[29] that a modification of the Einstein-Maxwell action can cause light to propagate at a speed faster than the speed of light defined by the metric, but this necessarily causes problems with causality and quantum mechanics.[30]

- Wikipedia

In other news, the speed of light in a vacuum REALLY SHOULD HAVE A NAME CHANGE. It is just *too* confusing sometimes, considering people often mess it up with the local speed of light in materials, for example. As well, the speed of light isn't limited just to light, but to all massless particles, but bleh.

It may be true for massive particles, where momentum is mass x velocity, but photons have no mass.

The equation still holds (e.g. p = h-bar*k, E = h-bar*w), althoug the equation of energy and momentum there is E^2 = (mc^2)^2 + (pc)^2, not E = pc as it is for massless particles. (As well, momentum is actually mv/sqrt(1-v^2/c^2) relativistically, and the quadratic E-P equation that I said earlier only accounts for relativity as well, but meh.)

EDIT: OMG! Its even worse now. It seems the wiki article on the planck temperature cites a NIST value, and we all know that NIST tables are NOT TO BE TRUSTED. Now I just have no idea what to believe!

To be fair, the idea of planck units is a matter of the order of the measurement, rather than the exact quantity of unit.

 

[Mise]

@Bill: My point was that the HUP is an uncertainty relation between position and momentum, not velocity. The distinction is important when dealing with photons, whose momentum is not related to its velocity, but to its wavevector.

Also,

the speed of light in a vacuum REALLY SHOULD HAVE A NAME CHANGE

How about c?

 

[Bill3000]

Ah, yes, I know. I had argued (...more like lecture) with someone over that for quite a while a couple months ago. As to regarding the speed - meh. How about the word that "c" came from? (I believe celestis) Or, barring that, Einstien's Constant?