Speed of light

[tballou]

Can anyone provide a relatively brief answer or send a link that addresses why the speed of light is 300,000 kps, and not some other faster or slower speed? Why 300,000 kps and not 200,000 or 400,000? Thanks in advance!

[apodman]

Can anyone provide a relatively brief answer ...

(my bold) haha

... why the speed of light is 300,000 kps, and not ... 200,000 or 400,000?

To quote Walter Cronkite, "That's the way it is."

One way, c (the speed of light in free space) can be measured experimentally, and that's what it comes out to be.

Another way, c is equal to the square root of the product of e0 and u0 (really lowercase epsilon and mu with zero subscripts), where e0 is the electric permittivity of free space and u0 is the magnetic permeability of free space. Light is an electromagnetic wave with electric and magnetic components, and e0 and u0 quantify the interaction between the wave and the space. You asked for a short answer, so the terms in that description are a bit loose. For more detail, start with Maxwell's equations.

Note that in a non-vacuum medium, permittivity and permeability values are lower and so is the speed of light. The reduced speed of light in a material like glass produces refraction; this allows us to make lenses, make telescopes, and see the stars.

[Chris Peterson]

Can anyone provide a relatively brief answer or send a link that addresses why the speed of light is 300,000 kps, and not some other faster or slower speed? Why 300,000 kps and not 200,000 or 400,000? Thanks in advance!

The question is not answerable using any existing theory, and is likely not answerable at all. Physical constants are what they are because the structure of the Universe is what it is. Eventually, it's likely that some physical constants will be found to be dependent on others, but there will still be a set of fundamental constants. Asking "why" they are what they are is probably a meaningless question.

[astrolabe]

Hello Chris or apodman,

In a few recent posts it mentioned that DM affects normal matter.I wanted to ask at that time if it was in fact the other way around but kept forgetting until now. Maybe the effects of these two states of matter if they are different are mutual?

[Chris Peterson]

In a few recent posts it mentioned that DM affects normal matter. I wanted to ask at that time if it was in fact the other way around but kept forgetting until now.

When it comes to gravity, there's no difference between A affecting B and B affecting A. That is, any two particles that interact gravitationally experience the same force (and this can be extended to any number of particles). So it seems virtually certain that dark matter is influenced by normal matter as well. It's customary to say it the other way around simply because that's how we generally observe it, and also because the total mass of dark matter is much greater than the total mass of normal matter.

There's no reason to think that Newton's laws of motion don't apply to dark matter (particularly the 3rd Law in this case).

[astrolabe]

Hello Chris,

Beautiful even when invisible. Thank you.

[tballou]

Given that E = m c2, does this not mean that c = square root of E/m, or more generally that c is determined by the ratio of energy and matter (whatever that means)?

And along these same lines, is there an equivalency between E = mc2 and F = m a? m should be the same in each equation, and is c2 an expression of acceleration?

Just wondering.

[apodman]

Given that E=mc², does this not mean that c = square root of E/m, or more generally that c is determined by the ratio of energy and matter (whatever that means)?

Yes (actually "energy and mass", not "energy and matter"), and it applies to "Energy-Mass Equivalence". See ...

http://en.wikipedia.org/wiki/Mass-energy_equivalence

... which says something about "whatever that means".

Forgot to mention that one. Amazing how you come at c from another angle and get the same thing. That's what I call one of the real wonders of nature. Mass-energy equivalence is more on the minds of the particle (quantum mechanical) crowd, whereas in this forum I see more propagation-of-light discussion; hence my bias toward the e0 u0 and overlooking the mc².

is there an equivalency between E=mc² and F=ma?

You're sort of on the right track.

Compared to Force (F), Energy (E) has an extra factor of Length.
Force is mass·length/time², whereas Energy is mass·length²/time².

This is the same extra factor of Length that v² has over a.
Acceleration (a) is length/time², whereas Velocity squared (v² or c²) is length²/time².

So that is how an Energy equation with a factor of v² or c² relates to a Force equation with a factor of a.

The formula for the Kinetic Energy of a particle or object moving at Velocity v is "E=½mv²".
This is independent of how suddenly or gradually or by what force it was accelerated to this velocity.
When v=c, the Kinetic Energy without the benefit of relativity would be "E=½mc²".
This is half as large as what you get from Einstein's Energy-Mass equivalence formula "E=mc²".
I know that doesn't explain it, but hopefully it sketches out what you're dealing with.

Once again, short explanations mean loose descriptions.

[tballou]

To Apodman - thanks so much for your insights on this!

[Chris Peterson]

Given that E = m c2, does this not mean that c = square root of E/m, or more generally that c is determined by the ratio of energy and matter (whatever that means)?

You're on the edge of a tautological argument here. If 12 = 3 * 4, does that mean that '3', in some fundamental way, is 'determined' by the ratio of '12' and '4'?

c is not the speed of light. c is a physical constant (in fact, a universal constant), that shows up in many areas. One example is that it is the constant of proportionality between energy and mass. It is seen in electromagnetic constants, nuclear constants, and elsewhere. It so happens that the velocity of light never exceeds c, and equals it in a vacuum. But that is just one of the physical manifestations of this constant, as is E = mc^2. I don't think you can say it is 'determined' by anything.

[makc]

Can anyone provide a relatively brief answer or send a link that addresses why the speed of light is 300,000 kps, and not some other faster or slower speed? Why 300,000 kps and not 200,000 or 400,000? Thanks in advance!

That would have to be me, again, quoting SI brochure section 2.1.1.1:

The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.
It follows that the speed of light in vacuum is exactly 299 792 458 metres per second

This is by definition. If you were to use light seconds as units of length, you'd have c = 1.

[bicyclebones]

I am an artist and not a physicicst so please don't take my comments literally because I only seek to stimulate thought in the minds of those who have the knowledge it will take to know the reality, so I ask if the escape velocity from a black hole is greater than the velocity of light then gravity must have a greater velocity than light because we see the effect of the gravity of a black hole but can't see the light. Black holes can come in any size, why think they must have an emminant demise, rather there is room inside of space where a trillion suns can hide without a trace.

[makc]

better to say that there is no velocity enough to escape from there (from "beyond the horizon"). it is not, however, quite clear (to me), how is it possible to get there in the 1st place.

[Qev]

Well, from the perspective of General Relativity, gravity isn't a thing that moves through spacetime, but is rather a change in the shape of spacetime itself caused by the mass of the black hole. That bending of space is what we experience as gravity. Gravitational waves apparently move at the speed of light, but again, they're not things, they're changes in how spacetime is bending.

[bicyclebones]

Yet Chris Petersen has reminded me that there are collectors being built to detect gravity waves. Maybe what gravity is shaping is only part of what exists in space like the meduim that carrys elcetro magnetic waves. Possibly there is more to space than what light interacts with and maybe gravity does not affect that type of space. I have gut feelings that there is more to gravity being a distortion or shaping of space time. I wonder if it just curves part of the things space is filled with. We need to know more about gravity.

[stkegg]

Obtaining E=mc^2 from Newton’s F=am in 10 steps

1) Force = Mass x Acceleration <-- Original Newton equation

2) Work = Force x Distance

As Energy = Work, then replacing Energy in 2) we have:

3) Energy = Force x Distance

Also, Force = Mass x Acceleration, then replacing Force in 3) we have:

4) Energy = Mass x Acceleration x Distance

But as Acceleration = Speed/Time and Speed = Distance/Time we can say that:
Acceleration = Distance/Time/Time or Distance/(Time^2). Then, replacing Acceleration in 4) we have:

5) Energy = Mass x (Distance/(Time^2)) x Distance

Or, by combining Distance into a square, we have:

6) Energy = Mass x (Distance^2) / (Time ^2)

Splitting the squares

7) Energy = Mass x (Distance/Time) x (Distance/Time)

Since Distance/Time = Speed, we can say

8 ) Energy = Mass x Speed x Speed

Or

9) Energy = Mass x Speed^2

If Speed = speed of light (c), then

10) Energy = Mass x c^2 <-- Original Einstein equation


What did Einstein ‘invent’?

[neufer]

9) Energy = Mass x Speed^2

If Speed = speed of light (c), then

10) Energy = Mass x c^2 <-- Original Einstein equation

What did Einstein ‘invent’?

Speed = c = constant

Mass = (rest mass)/sqrt[1-(v/c)^2]

[Chris Peterson]

Obtaining E=mc^2 from Newton’s F=am in 10 steps...

9) Energy = Mass x Speed^2

If Speed = speed of light (c), then

10) Energy = Mass x c^2 <-- Original Einstein equation

There's the weak point. Why do you make this assumption? When we consider mass-energy equivalence, there is no obvious choice for velocity.

What did Einstein ‘invent’?

He didn't "invent" anything. The Universe did that. Einstein "discovered" a mass-energy equivalence formula (although others were heading in the same direction). Einstein made things work by considering the relativistic momentum of a particle- which is where c enters the equation.

[apodman]

On first glance, it appears that you multiplied instead of integrating and are off by a factor of 2 when you get to step 5.

I also don't see where a photon gets an acceleration term.

Is this just a bunch of ingredients thrown together without physical meaning?

[aristarchusinexile]

Consider that time runs faster the higher up we go in a gravity field, speed of light in relation to sea level time will increase the further 'up' we go, therefore, once we escape gravity fields completely, (not just earth's field, or the sun's field, or our group of galaxy's field .. but all gravity fields .. and there will be such a place in space where gravity does not exist because gravity is such a weak force that it cannot even account for the shape of spiral galaxies .. light will travel instantaneously to the next gravity field, where time will again effect it, slowing it down, until at the lowest point of the gravity field it will cease to travel .. be at a standstill. Light travelling 'instantaneously' is not the same as light travelling at infinte speed, as infinity is a measurement, whereas instantantous is not measurable. By the way, Einstein never said the speed of light is constant, he said it should be raised to a level of constancy for work in inertial systems. Outside of a gravity field there will be no inertia. Knowing that light travels instantaneously will rewrite many measurements of distance, will render obsolete many concepts. In fact, the effects of time seem to be almost totally underfactored in most people's concepts of how the universe works. Jets from black holes, for instance, gaining energy the further out they go, could result simply from escaping the constraints of time and light slowed to a standstill by the gravity of the black hole .. the further out from the hole the jet goes, the faster time runs, so the more energy is 'gained' by the jet.

[Chris Peterson]

Consider that time runs faster the higher up we go in a gravity field, speed of light in relation to sea level time will increase the further 'up' we go...

The speed of light doesn't change. Space and time are locked together; while the rate a clock runs changes, so does the spatial metric.

[Doum]

Consider that time runs faster the higher up we go in a gravity field, speed of light in relation to sea level time will increase the further 'up' we go, therefore, once we escape gravity fields completely, (not just earth's field, or the sun's field, or our group of galaxy's field .. but all gravity fields .. and there will be such a place in space where gravity does not exist because gravity is such a weak force that it cannot even account for the shape of spiral galaxies .. light will travel instantaneously to the next gravity field, where time will again effect it, slowing it down, until at the lowest point of the gravity field it will cease to travel .. be at a standstill. Light travelling 'instantaneously' is not the same as light travelling at infinte speed, as infinity is a measurement, whereas instantantous is not measurable. By the way, Einstein never said the speed of light is constant, he said it should be raised to a level of constancy for work in inertial systems. Outside of a gravity field there will be no inertia. Knowing that light travels instantaneously will rewrite many measurements of distance, will render obsolete many concepts. In fact, the effects of time seem to be almost totally underfactored in most people's concepts of how the universe works. Jets from black holes, for instance, gaining energy the further out they go, could result simply from escaping the constraints of time and light slowed to a standstill by the gravity of the black hole .. the further out from the hole the jet goes, the faster time runs, so the more energy is 'gained' by the jet.

Where such a free environment of gravity field reside. Because for now where ever we look we see the gravity field effect everywhere. All i read up to now is that the gravity field extand to infinity. It may be weak at some place but it is there even if weak. And dark matter seem to exist and also have a gravlty field. I'm curious about that new theory? Did i see you before?

[aristarchusinexile]

Consider that time runs faster the higher up we go in a gravity field, speed of light in relation to sea level time will increase the further 'up' we go...

The speed of light doesn't change. Space and time are locked together; while the rate a clock runs changes, so does the spatial metric.

If space and time were locked time would not alter so quickly and at such infinitesimal distances on the cosmological scale. Time and space are separate entities co-existing for mutual benefit at times in some spaces, but capable of existing separately from each other, and because they are capable of doing so, they do so, in some times and in some spaces.

[aristarchusinexile]

Where such a free environment of gravity field reside. Because for now where ever we look we see the gravity field effect everywhere. All i read up to now is that the gravity field extand to infinity. It may be weak at some place but it is there even if weak. And dark matter seem to exist and also have a gravlty field. I'm curious about that new theory? Did i see you before?

Perhaps you glanced with those binoculars into history? You read that gravity exists everywhere? Do you believe everything you read? Doum, gravity is so weak that 'it is said' that galaxies cannot be held together by it, so Dark Matter was theorized as accounting for the shape of spiral gravities. If gravity is so weak, how can it extend to infinity? Gravity weakens the further removed from its source it is 'measured' .. therefore, mathematically, it must become so weak so quickly as to disappear entirely, again, quickly. Of ocurse we're discussing the question of, 'if two tiny entities existed nearly infintely apart, would they find each other?' That question could be answered in many other ways besides gravity .. and why should they have to find each other at all? Why can't they just go off on their own separate existance? Movement within chaos does not have to eventually result in two entities coming together as some theories of gravity suggest .. solitude is an ordered part of existance.

[bystander]

If space and time were locked time would not alter so quickly and at such infinitesimal distances on the cosmological scale. Time and space are separate entities co-existing for mutual benefit at times in some spaces, but capable of existing separately from each other, and because they are capable of doing so, they do so, in some times and in some spaces.

From Wikipedia: Spacetime

• In classical mechanics, the use of Euclidean space instead of spacetime is appropriate, as time is treated as universal and constant, being independent of the state of motion of an observer. In relativistic contexts, however, time cannot be separated from the three dimensions of space, because the rate at which time passes depends on an object's velocity relative to the speed of light and also the strength of intense gravitational fields which can slow the passage of time.