# Is the speed of light a velocity or acceleration?

1. Jun 4, 2009

### ryuunoseika

Since light speed requires an infinite amount of time to achieve it's effectively an acceleration right? Does anyone know what I'm trying to say? And better yet, if it's right?

2. Jun 4, 2009

### Mentz114

1. Acceleration is the derivative of velocity wrt time.
2. A massless thing can accelerate to c in zero time.

3. Jun 5, 2009

### MeJennifer

A massless thing always travels at c so it never really accelerates.

4. Jun 5, 2009

### fatra2

You answered your question right there. The speed of light is a speed/velocity. It indicates the distance travelled by a photon.

Remember, that c is the distance travelled by a photon in vaccuum. Light and other electromagnetic radiation will have different speed in different matters.

Cheers

5. Jun 5, 2009

### atyy

A massive particle can never achieve the speed of light, so if it tries to, it will accelerate forever.

A massless particle travels at the speed of light, never accelerating or decelerating.

6. Jun 5, 2009

### malawi_glenn

speed has the units of velocity so it is clearly a velocity.

7. Jun 5, 2009

### fatra2

Hi there,

Not really. Since the accelaration is define as $$\frac{dv}{dt}$$, if the speed of the particle/object stops increasing, its acceleration follows with.

I agree that to accelerate a massive object that is close to the speed of light is very hard. But this is due to the increase in mass: $$F = \frac{dp}{dt} = \frac{d(mv)}{dt}$$. This is the reason why a massive object cannot reach the speed of light.

Cheers

8. Jun 6, 2009

wrong.

9. Jun 6, 2009

### ryuunoseika

Nvm, no one understands what im saying. I didnt really phrase it right.

10. Jun 6, 2009

### tiny-tim

Hi ryuunoseika!
Yes, if you try to accelerate up to the speed of light, however long you take, you will never quite reach the speed of light …

so in that sense light speed does require an infinite amount of time to achieve.

But it's not an acceleration …

it doesn't move away as you're trying to catch it!

11. Jun 7, 2009

### Naty1

ryuu...
mejen posted one view for massless particles; tiny-tim the other side for particles with mass....in any case your statement which I quoted implied equating velocity and
acceleration....that can't be done, it's just never true...acceleration is the rate of change of velocity....they measure two different, but related, variables....

12. Jun 7, 2009

### DrGreg

I found this quite baffling. After all, speed is measured in m/s and acceleration in m/s2, so how can a speed be an acceleration?

But then tiny-tim said this:

Then I realised what you were thinking.

If you are accelerating, trying to catch up with a photon, you find that the speed of the photon is still c. From your point of view, it appears that the photon is accelerating as you accelerate, so that the difference in speeds remains constant.

But this is an illusion, based on the assumption that it is valid to subtract speeds.

You actually need to use the formula

$$\frac{u - v}{1 - uv/c^2}$$​

There is another way to measure motion in relativity, and that is "rapidity".

The relationship between speed v and rapidity ϕ (measured in the same units as speed) is given by the equation

$$\frac {v}{c} = \tanh \frac{\phi}{c} = \frac {e^{\phi/c} - e^{\phi/c}} {e^{\phi/c} + e^{\phi/c}}$$​

That may look complicated, but rapidity has lots of nice properties compared with speed.

1. For objects all moving in the same straight line, rapidities can be added and subtracted.
2. The rapidity of light is infinite.
3. At low speeds, rapidity and speed are approximately the same.
4. For an object undergoing constant proper acceleration α (as measured by its own accelerometer), rapidity increases linearly with proper time τ (as measured by its own clock), ϕ = ατ

Looked at from this point of view, the rapidity of light isn't an acceleration, it's just infinite so no wonder you can't reach it.

Technical note: I've deliberately chosen to define rapidity with the dimensions of speed, but many authors define it dimensionlessly via $v = c \tanh \phi$

Last edited: Jun 7, 2009
13. Jun 7, 2009

### ryuunoseika

No, no, i understand that acceleration is a term for change in velocity over change in time, and that velocity is merely the derivative of an acceleration function. All i did was poorly phrase my question; i was very tired when i posted it and, admittedly, not of sound mind.

I was think in terms of velocity and acceleration which was counter-compensated for the lorentz transformation (i.e. The speed of light is infinity) to describe velocity from the perspective of the accelerating body. Its an absurd way of looking at things and it produces unreasonable results. I have no idea why i was using it, and I withdraw my question as i later answered it on my own.

14. Jun 7, 2009

### dsmith23

this is not true: consider the electromagnetic spectrum. all of these waves are exactly the same, at least in what you might consider to be the wave 'quality.' the only thing that changes proportionately is their frequency and wavelength. light makes up a very small part of this spectrum falling under the visible light category. just because radio waves for example are massless, this does not mean that they move anywhere near the speed of light. especially because even looking at different colors of light, they all have different wavelengths and thus move slightly faster or slower than one another.

15. Jun 7, 2009

### tiny-tim

Welcome to PF!

Hi dsmith23! Welcome to PF!
Yes, that's true in a material (air, glass, etc), but not in a vacuum

in a vacuum, all colours, and radio waves etc, go at the same speed (c).

16. Jun 7, 2009

### DrGreg

All electromagnetic waves travel in vacuum at the same speed c. The wavelengths λ and frequencies f all vary, but the speed remains constant.

$$c = f \lambda$$​

17. Jun 10, 2009

### MeJennifer

I second that!

18. Jun 10, 2009

### Damos

I like to think that the mass gained by an object as it approaches the speed of light is basically a resistance to it's acceleration. So maybe massive particles can travel at the speed light, the problem is accelerating to such a speed.
isn't this the same as the resistance of a massive particle to accelerate in space time at low velocities, except, at high speed the resistance is plotted on an expotantial curve rather than a linear one?

19. Jun 15, 2009

### fatra2

Hi there,

What you are describing here is the definition of inertia, and not the increase of mass at very high speed.

And who is talking about exponential instead of linear. If you look at the mass increase of an object, you will see that the exponent never appears into it, but rather a square.

Cheers