travelling at the spead of light

[t00fri]

Spiff,

you presumably mean negative mass^2, i.e. imaginary mass.

...
Anyways, I thought an imaginary mass squared would give a negative mass,

Sorry: the square of an imaginary mass gives a negative mass^2!

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(i*m)^2 = - m^2;   m real


But I can see now what you and|or your former lecturer had in mind: you|he were specializing on gravity, while I considered a generic situation in particle physics, instead.

I suppose the (naive) idea was to make use of the sign of a mass to switch between gravitational attraction and repulsion...In particle physics the sign of the mass has NO physical meaning, while the sign of the mass^2 has.

The mass shell is just a kinematical configuration (E,p,m) of a particle satisfying the relativistic energy-momentum condition:

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E^2=p^2 + m^2;    (h-bar=c=1)     (*)


In a plot of E versus (p1,p2,p3), the mass-shell condition (*) just represents a hyperbolic shell (surface). For m=0, this surface degenerates to the so-called 'light cone' E^2=p^2. Just try and draw a respective figure yourself....

As to the rest: ...I am too tired tonight. I had a long day and leave the matter to a professional astro-physicist as required by Fightspit above

Bye Fridger

[Fightspit]

Still want an astro-physicist??

No, I don't, because I will be on first year of Engineer Electronic's School but I am interisting about physic.

[Le Chacal]

Argh... What a headache !

Negative mass, kinetic energy without mass...

But what about the theory of particles with negative energy, like tachyons, which in theory decelerate to the speed of light when they gain energy ?

(non please, don't hit me on the head)

I know it's not the subject, but this theory was developped in the past, no ? (in the 70's I think)

[Spaceman Spiff]

I think it is preferable to have an Astro-physician ...

I think t00fri's right that a particle physicist would be better for explaining relativity, astrophysicists usually get away without using relativity in their field. Cosmologist might be what you were thinking, but it seems they're getting closer with the particle physicists.

Since Cham's perturbed my confidence in understanding relativity (because he may be right that I'm wrong, I just can't see it very clearly), I've looked for references, and I think wikipedia does seem to be a very good, concise source. See the entry on Wikipedia: Special Relativity ( http://en.wikipedia.org/wiki/Special_relativity ).

I think it also shows that 'our' mistake is not simply redirecting someone like GoHeelsWeeeehoooo there in the first place. It's a lot less work that way. It's better than risk having someone explain it all wrongly.

Spiff.

[Andy74]

Fridger,

if you're able to restore your mini-lecture, then could you please post it?
I think there are many people who could benefit from it ...
Thank you.
Have a nice week-end (with maybe a beer or two?).

Andy

[Spaceman Spiff]

Sorry: the square of an imaginary mass gives a negative mass^2!

There's that ^2 again... Imaginary number squared equals negative number squared? Yes, the lecturer was talking about just gravity, but I shall take into account:

As to the rest: ...I am too tired tonight.

The Wiki link above takes care of it...

Spiff.

[Spaceman Spiff]

But what about the theory of particles with negative energy, like tachyons, which in theory decelerate to the speed of light when they gain energy ?

This goes with my collection of strange utterances I've heard from physics lecturers, things they mention on the side, but never put into their lecture notes... Two I've mentioned already:

- "Photons exhibit FTL action at a distance in quantum mechanics because they see the universe with zero depth and everything happens all at once for them."

- "It's theoretically possible for there to be negative mass, though we never find any."

I was just wondering if there are any good reasons why such statements might be discarded/entertained (which if why I wrote "Or so it seems" after mentioning the first one right on page 1 of thios topic...).

Spiff

[Spaceman Spiff]

Here's how I see it ...

chaos, I say thanks! for that. It looks to me like you've summarised very well what I think Cham was trying to say, and made the argument clearly enough such that I might be able to see whether I'm wrong. I'm not yet saying that I am wrong, because I want to check some more maths, and that requires that I go away and work some things out by myself.

I'm going to check whether ??.m0 for v = c and m0 = 0 (or 0 * INF as it's being written in 'shorthand' here) is truly undefined, or is zero, or one, or whatever. See, is the sinc(x) function is undefined at x = 0?

I'll also read up more wikipedia stuff.

Meantime, to all, I'm afraid I'll have to be offline for the remainder of the month, as I have to perform some calculations of an order of magnitude greater complexity than either Special or General Relativity, Quantum Mechanics, or even a Grand Unified Theory of Everything... It's called an Einkommensteuererkl?¤rung.

I'll report afterwards.

Spiff.

[t00fri]

There's that ^2 again... Imaginary number squared equals negative number squared?
...
Spiff.

Spiff,

please don't forget that a mass is not a number but a dimensionful quantity!

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i * i = -1

and

(i*m) * (i*m) = - m^2


No doubt that this is correct
Bye Fridger

[Spaceman Spiff]

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(i*m) * (i*m) = - m^2


Alles klar!

Spiff.

[ajtribick]

chaos, I say thanks! for that.

You're welcome

I'm going to check whether ??.m0 for v = c and m0 = 0 (or 0 * INF as it's being written in 'shorthand' here) is truly undefined, or is zero, or one, or whatever. See, is the sinc(x) function is undefined at x = 0?

The sinc(x) function is defined as sinc(x)=sin(x)/x when x=0, sinc(x)=1 at x=0, this latter part ensures the function is continuous.

The reason I said that 0*??? is not well defined becomes clear when we consider several different functions which become 0*??? at x=0:

f(x)=0*(1/x)
g(x)=x*(1/x)
h(x)=x*(1/x??)

At x=0, all of these functions have a result which is 0*???. Investigating the limit as x tends to zero reveals that f(x) tends to 0, g(x) tends to 1, and h(x) tends to +??? or -??? depending on the direction from which you approach the limit!

Similarly, for the quantity ??m0, we can approach the expression for a photon by starting with m0=0 and allowing v to tend to c, in which case the limit is 0, or we can approach the expression for a photon by starting with v=c, and allowing m0 to tend to 0 (from positive values), in which case the limit is ???. You can also approach it by a mixture of these two methods, but I'm not going into that now, because you get the general drift.

This is what I mean by the quantity being not well defined!

(I hope this explanation is correct, but when dealing with infinities and limits like this it is very easy to make mistakes - I'm not entirely sure if everything I've said in this post is valid. Please correct me if I'm wrong!)

[maxim]

Just a stupid question:

vphoton = c (in vacuum)
vphoton < c (in matter, with different v for different kind of matter)

Can we construct/imagine a matter where vphoton -> 0?

maxim

[Cham]

Just a stupid question:

vphoton = c (in vacuum)
vphoton < c (in matter, with different v for different kind of matter)


Can we construct/imagine a matter where vphoton -> 0?

maxim

You mean v > c ?

No, it would violate causality.

[maxim]

No, I mean v << c with lim(v)->0

maxim

[Scytale]

The speed of the photon is never different than c. The speed of the light wave might be lower than c in certain media because of refraction, but photons' speed is always c.

[t00fri]

...
The sinc(x) function is defined as sinc(x)=sin(x)/x when x=0, sinc(x)=1 at x=0, this latter part ensures the function is continuous.
...

There are typically two quick ways to determine the limit of

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f(x) = g(x)/h(x) with  g(x), h(x) -> 0 near x -> 0



a) Consider the leading terms of a (Taylor) series expansion of g(x), h(x) around x=0:

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g(x) = sin(x) = x + O(x^3)
h(x) = x

f(x) = g(x)/h(x) ~ x/x = 1


b) remember the h??pital rule:

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limit(x->0, f(x)) = limit (x->0, diff(g(x),x))/limit(x->0, diff(h(x),x))


in case of f(x) = sinc(x), this means

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diff(sin(x),x) = cos(x) -> 1 for x = 0
diff(x,x) = 1  -> 1 for x -> 0

hence

limit (x->0,sinc(x)) = 1



Bye Fridger

[Ptarmigan]

Can we construct/imagine a matter where vphoton -> 0?

Bose-Einstein condensate is one way,
in 1999 17 m/s by Hau, Harris, Dutton, and Behroozi.
Others since then have slowed it even further. 1 cm/s I think in 2004, not sure what the latest state of play is.

[Spaceman Spiff]

Fridger,

you're "totally" on the right track already: that it can be mathematically proven that sinc(0) = 1, that is is not just defined like that.

I just want to sit down and apply that to the Lorentz transform.

And the relevance: does SR predict or assume m0 = 0 for photons? Which was what BlindedByTheLight was asking...

Spiff.

[Spaceman Spiff]

construct/imagine a matter where vphoton -> 0?

.... and I read of something called 'frozen light'.

I must go now.

Spiff.

[t00fri]

Fridger,

you're "totally" on the right track already: that it can be mathematically proven that sinc(0) = 1, that is is not just defined like that.

...
Spiff.

I hope so . I also happen to have a math degree...

Bye Fridger