Galaxies

[Naraoia]

Mass increases as you approach c as a function of your existing mass and the fraction of c that you travel. If you're mass is 0, then you have no mass either at 0c or 1c.

Your existing mass or your rest mass?

I've always kind of assumed that it's massless nature is what allows a photon to both travel at the speed of light and not travel at a speed less than that.

Yes, that's fine, but...

One thing I've never understood is this:

E=mc^2

E=(0)c^2=0

So the energy of a photon = 0

If you approach it from the other end and start with the assumption that a photon does have energy, then the inevitable conclusion is that a photon also has mass (of some kind).

(However, isn't E = mc[sup]2[/sup] a special case of a more complicated equation? Been a while since I opened that relativity textbook :o)

 

[ragarth]

Google searching brought this up: http://www.weburbia1.demon.co.uk/physics/ParticleAndNuclear/photon_mass.html

Basically, a photon does indeed travel at the speed of light due to a lack of mass, however it does contain relativistic mass. This is theoretical, since we can't bring a photon to a resting state, we cannot measure it's resting mass, but instead can only put upper boundaries on it based upon observation of other phenomena.

Working with this equation:

E[sup]2[/sup] = p[sup]2[/sup]c[sup]2[/sup] + m[sub]rest[/sub][sup]2[/sup]c[sup]4[/sup]

where E=Energy
p = m[sub]rel[/sub]*v
m[sub]rest[/sub]=resting mass
c = light speed (naturally)
v = velocity
and m[sub]rel[/sub] = relative mass

Then the Energy of a photon is:
E=pc

Plugging in the value of p we get:
E=m[sub]rel[/sub]*vc

and solve it for m[sub]rel[/sub]
m[sub]rel[/sub]=E/vc which (correct me if I'm wrong) is: m[sub]rel[/sub]=E/c[sup]2[/sup]

If we use this graph: http://hyperphysics.phy-astr.gsu.edu/HBASE/mod2.html Then we can find a value for E which will give a non-zero value for m[sub]rel[/sub] even though m[sub]rest[/sub] is 0.

 

[Wiccan_Child]

It doesn't have a rest mass. Does that automatically mean that it also doesn't have mass due to its movement?

Some people interpret it that way, but I don't. It's like the various interpretations of quantum mechanics; none is right, they're just different ways of understanding the same phenomenon.

Argh. I actually have a textbook on special and general relativity. And a good one at that, though my resolve to work through it didn't last very long. Maybe I should pick it up again.

Textbooks are good, but they have so much text! Eurgh.

(However, isn't E = mc[sup]2[/sup] a special case of a more complicated equation? Been a while since I opened that relativity textbook :o)

As ragarth said, the special case is E[sup]2[/sup] = p[sup]2[/sup]c[sup]2[/sup] + m[sup]2[/sup]c[sup]4[/sup]. When the particle isn't moving, p = 0, so we're left with E[sup]2[/sup] = m[sup]2[/sup]c[sup]4[/sup]. Or, E = mc[sup]2[/sup].

 

[Wiccan_Child]

I've interpreted relativity the same way as Naroia. Since a photon travels at or near the speed of light (Keep in mind that the speed of light changes based upon the medium and the frequency of the lightwave), then it has no actual perception of time even though we perceive time in the photon's movements. Let's do a thought expirement:

Our photon is now a yellow submarine. At the photon factory it's loaded up with a days worth of supplies and two people, and then it's launched out into the universe at the speed of light in a vacuum. Our yellow photon submarine will travel for eternity or until it's either absorbed by a particle or something happens to cease it's existence, and our people will never complete their first breath, first sip, or first drink of their stored supplies because time has effectively stopped for them. The photon continues to move, however, because even though time on the submarine has stopped, external time has not and so we will perceive it's motion even though the people on the submarine do not.

Yes, but submarines have mass I am of the opinion that photons do experience time, just in a very weird way. There has to be some perception of time, otherwise all events would happen simultaneously, and they would have all energies and no energy, and crazy things would happen.

That is, how can a photon change energy if it doesn't experience time?

 

[Wiccan_Child]

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[Wiccan_Child]

Maybe that's why science gets such a bad Rep...

It does? I thought it was upheld as a glorious beacon of salvation and grace .

In my experience, laymen see science as this thing which answers questions. They don't try to fathom the esoteric mutterings of scientists though, because it looks so damn complicated

The Earth doesn't necessarily orbit the Sun.........[wash my mouth][wash my mouth][wash my mouth].....

Since when?

Since forever. Remember that Galileo only refuted the notion that all celestial bodies orbit the Earth, not that the Earth is the centre of the universe, but everything has their 'usual' orbits about the Sun (which in turn orbits the Earth).

General relativity tells us that no frame of reference is special, so we can pick our origin to be whatever we feel like. If we choose the Earth to be our origin, so be it.

OK, if it isn't necessarily orbit the sun what the hell is it orbiting?

Is the Moon orbiting the Earth, or is that an illusion too?

It depends on where you're sitting. If we sit on the Moon, the Earth orbits us. If we sit on the Earth, the Moon orbits us. If we sit in the centre of mass of this two-body system, they both orbit us.

Where we sit is arbitrary, and there is no 'special' set-up. There's no real reason to say that the Moon orbits the Earth, except that we have evolved to take the large, heavier thing as being stationary, with everything moving around it.

 

[ragarth]

Yes, but submarines have mass I am of the opinion that photons do experience time, just in a very weird way. There has to be some perception of time, otherwise all events would happen simultaneously, and they would have all energies and no energy, and crazy things would happen.

That is, how can a photon change energy if it doesn't experience time?

What makes you think a photon changes energy? A photon's energy is defined by it's wavelength, and a photon's wavelength does not change. Rather, when we hit a surface with visible light and it emits infrared, it is absorbing the visible light and emitting new infrared photons. Further, a photon always travels at the same speed. In an absolute vacuum that is c, in a medium a photon's speed is defined by it's wavelength, which does not change.

Red and blue shift, by contrast is not the photon's wavelength changing, but rather an effect of doppler shift, so the perceived change is due to our perception of the photon based on our movement through space relative to the emitting body.

 

[Wiccan_Child]

What makes you think a photon changes energy? A photon's energy is defined by it's wavelength, and a photon's wavelength does not change. Rather, when we hit a surface with visible light and it emits infrared, it is absorbing the visible light and emitting new infrared photons.

Yes, I know. I was thinking more about changes to the photon itself as it passes through electromagnetic or gravitational potentials (â la gravitational red- and blue- shifts).

Further, a photon always travels at the same speed. In an absolute vacuum that is c, in a medium a photon's speed is defined by it's wavelength, which does not change.

Red and blue shift, by contrast is not the photon's wavelength changing, but rather an effect of doppler shift, so the perceived change is due to our perception of the photon based on our movement through space relative to the emitting body.

Actually, since its energy is E=hf, it would indeed change in energy. There are more ways to change a photon's frequency than absorption/emmision, or relative motion.​

 

[Allister]

It depends on where you're sitting. If we sit on the Moon, the Earth orbits us. If we sit on the Earth, the Moon orbits us. If we sit in the centre of mass of this two-body system, they both orbit us.

You have seriously lost me....

Regardless of where we are sitting it is the Moon that orbits the Earth!! I always understood it to be heavier objects bending space and the lighter objects whirling around the dip in gravity. Hence the Sun orbiting the Core, the Earth and planets orbiting the Sun and the moons orbiting their respective planets....

Or is that a load of baloney.....?

 

[Allister]

We're just trying to explain to you that there is no objective "default" frame of reference in space.

I know, and thanks for taking the time to explain, same to you WC. It's appreciated.

I follow the idea that there is no "default" frame of reference in space. Can we not though atribute greater importance to certain objects, objects that actively influence others.

Take the cars speeding along, one at 80mph, one and 70mph. Neither of these are actually interacting with each other so to say that the care behind is only going at 10mph makes little sense to me. When in fact distance (miles) are being covered in time (hour).

 

[Hespera]

You have seriously lost me....

Regardless of where we are sitting it is the Moon that orbits the Earth!! I always understood it to be heavier objects bending space and the lighter objects whirling around the dip in gravity. Hence the Sun orbiting the Core, the Earth and planets orbiting the Sun and the moons orbiting their respective planets....

Or is that a load of baloney.....?

I think this will clear things up for you.

http://www.youtube.com/watch?v=7mNjbA_Fguk

 

[ragarth]

Technically, the earth and moon do indeed orbit each other. The earth is massive enough compared to the moon that the point at which they spin around is inside the earth, but the earth wobbles as the moon spins around it, it's not completely still.

You can define your preferred point of reference based on anything. You may prefer to judge everything by what's the most massive, what has the most direct gravitational influence on you, or what has the purest shade of yellow. All movement is relative. We generally define our movement (mph or kph) based upon the planet, so the moon orbits the planet, cars travel along the planet, the sun rises and sets, etc. We define earth as the fixed point at which we measure all these things and assign their movement based upon that definition, regardless of the fact that the earth actually wobbles from the moon, or that it's surface is spinning and changing the cars velocity, or that the earth is orbiting the sun. All of those definitions of movement assume a different fixed point than the earth.

Take for instance, the term 'miles per hour' well, miles per hour from what? In relation to the planet's surface, 70miles. In relation to a galaxy, significantly more. You are putting 70 miles between you and a fixed point on the planet's surface every hour and many times more miles per hour between yourself and a distant galaxy every hour.

 

[Hespera]

I used to wonder what would happen if I could just hop offl, and have the earth rotate out from under me, and leave me behind. Combining the rotation speed, the orbital speed and the spinning of the galaxy, and the speed of wherever it is going... how fast would I go in what direction?

I still dont get it i guess. Makes me head spin no matter how i figure it. I guess I wouldnt be going anywhere, but this just isnt intuitive. Looking up into / down toward / in toward the center our galaxy is weird enough.

 

[Allister]

Technically, the earth and moon do indeed orbit each other. The earth is massive enough compared to the moon that the point at which they spin around is inside the earth, but the earth wobbles as the moon spins around it, it's not completely still.

Of course the Moon has an effect on the Earth, the wobbles, the tides etc... but as you said so much more eloquently than I, the Earth is the "centre of gravity" around which the Moon orbits.

Take for instance, the term 'miles per hour' well, miles per hour from what?

A mile is a finite distance regardless of "where it is". If we went into an empty patch of space we could theoretically lay down markers every mile. A mile doesn't have a fixed start other than the distance travelled until you reach an end.

Makes me head spin no matter how i figure it

I know how you feel...

 

[Naraoia]

Google searching brought this up: http://www.weburbia1.demon.co.uk/physics/ParticleAndNuclear/photon_mass.html

[...]

If we use this graph: http://hyperphysics.phy-astr.gsu.edu/HBASE/mod2.html Then we can find a value for E which will give a non-zero value for m[sub]rel[/sub] even though m[sub]rest[/sub] is 0.

Yeehaw! I'm so glad I'm not completely clueless about relativity

Some people interpret it that way, but I don't. It's like the various interpretations of quantum mechanics; none is right, they're just different ways of understanding the same phenomenon.

You might have a point there.

What I'm wondering now is if you take two points, send the photon from one to the other and calculate displacement along the t axis, what do you get? (If that question even makes sense)

Textbooks are good, but they have so much text! Eurgh.

Being rubbish at understanding written math without actually trying to apply it, I prefer my equations padded with explanation.

Yes, but submarines have mass I am of the opinion that photons do experience time, just in a very weird way. There has to be some perception of time, otherwise all events would happen simultaneously, and they would have all energies and no energy, and crazy things would happen.

That is, how can a photon change energy if it doesn't experience time?

Doesn't that notion of "simultaneous" depend on time as we perceive it? Couldn't a photon just have a different energy at various points of its trajectory in the same way a line can be thicker at one end than the other? I mean, even if it isn't displaced in time, the other three coordinates still change

(Now I'm trying to figure out how a line would perceive its own varying thickness. My brain refuses to cooperate.)

 

[Wiccan_Child]

You have seriously lost me....

Regardless of where we are sitting it is the Moon that orbits the Earth!! I always understood it to be heavier objects bending space and the lighter objects whirling around the dip in gravity. Hence the Sun orbiting the Core, the Earth and planets orbiting the Sun and the moons orbiting their respective planets....

Or is that a load of baloney.....?

Basically, yeah. The 'rubber sheet' model of gravity and spacetime is a conceptual aid, nothing more. The Sun exerts the greatest gravitational field in the Solar System, which is why everything (bar moons) orbit it, regardless of where you sit: if I take the Earth to be stationary, then the Sun and Moon orbit the Earth. However, the other planets still orbit the Sun! This is why it makes sense to arbitrarily call the Sun 'the centre'.

The Sun orbits the Earth just as the Earth orbits the Sun. It's just that it's so much heavier than the Earth that it is barely perturbed, and the centre-of-mass of the system lies within the Sun.

I know, and thanks for taking the time to explain, same to you WC. It's appreciated.

I follow the idea that there is no "default" frame of reference in space. Can we not though atribute greater importance to certain objects, objects that actively influence others.

Take the cars speeding along, one at 80mph, one and 70mph. Neither of these are actually interacting with each other so to say that the care behind is only going at 10mph makes little sense to me. When in fact distance (miles) are being covered in time (hour).

Only with respect to the road. You're making an instinctive assumption when you think about velocity as "how far you travel, divided by how long it took": you're taking the road to be stationary. Or, more precisely, you're taking your starting point to be stationary. That presumption is completely arbitrary; it is just as valid (though instinctively repulsive) to think of you as stationary, and your starting point (say, the garage) as moving away at 70mph.

 

[Wiccan_Child]

You might have a point there.

What I'm wondering now is if you take two points, send the photon from one to the other and calculate displacement along the t axis, what do you get? (If that question even makes sense)

If you were sitting at one of the points and measured the time it took for the photon to travel (through a vacuum) from you to the other point and back again, you would measure 2d/c.

That is, the time you measured would be two times the of the distance between the points d, divided by the speed of light c.

Being rubbish at understanding written math without actually trying to apply it, I prefer my equations padded with explanation.

Doesn't that notion of "simultaneous" depend on time as we perceive it?

To an extent. In special relativity, what are simultaneous to one person aren't necessarily simultaneous to another. A lot of the apparent paradoxes of special relativity are resolved that way. But this is something different to what I was talking about: events do not occur all at once, but instead are spread across space and time. With no sense of time, a photon would see everything happen at once.

Couldn't a photon just have a different energy at various points of its trajectory in the same way a line can be thicker at one end than the other? I mean, even if it isn't displaced in time, the other three coordinates still change

Yes, but change can only occur with time. No time, no change.

(Now I'm trying to figure out how a line would perceive its own varying thickness. My brain refuses to cooperate.)[/quote]
It would perceive it insofar as it is fundamentally described by its associated planar function. The 'line' is nothing more than an infinite number of points that satisfy some condition or rule (e.g., f(x) = x[sup]2[/sup]). B*gg*r*d if I know how to do that though .

 

[Naraoia]

Yes, but change can only occur with time. No time, no change.

Ok, I used the wrong word. "Difference" doesn't imply time.

It would perceive it insofar as it is fundamentally described by its associated planar function. The 'line' is nothing more than an infinite number of points that satisfy some condition or rule (e.g., f(x) = x[sup]2[/sup]). B*gg*r*d if I know how to do that though .

Oops, I should be more careful with my terminology... "line" was meant to be more like something you draw on paper, an actual two-dimensional thing with thickness, than the one-dimensional thing from geometry.

Not that it changes things that much.

 

[Wiccan_Child]

Ok, I used the wrong word. "Difference" doesn't imply time.

Either way, the problem remains: change is where a given point differs over time. It doesn't matter whether you call it "change" or "difference"; the fact that one is not the same as the other is sufficient to show the existence of time.

Oops, I should be more careful with my terminology... "line" was meant to be more like something you draw on paper, an actual two-dimensional thing with thickness, than the one-dimensional thing from geometry.

Not that it changes things that much.

I know, I'm just a mathematical pedant .

 

[Naraoia]

Either way, the problem remains: change is where a given point differs over time. It doesn't matter whether you call it "change" or "difference"; the fact that one is not the same as the other is sufficient to show the existence of time.

Uh... I'm not sure I get this. It sounds a bit like my fingers must be temporally distinct from my toes just because they aren't exactly identical. Or do you just mean single-component systems like particles? But particles aren't really indivisible either (though for all I know, maybe a photon is).

My poor little head is spinning.

I know, I'm just a mathematical pedant .