# The Speed of Light - Nothing can go faster?

#### Passionflower

Wrt sb?

If the person inside the craft has a drive that can push 3333G per second (that is, 30km/s^2). That means that in 10 000 seconds of HIS TIME he will reach speed of light. Whatever THAT means. It says on the darn user manual :) And my problem is, I see nothing preventing him from doing that except flattening of space. In some explanations of "fast movement" it is noted that the observer inside the craft does not see much out of the ordinary it his reference frame.
...
Sorry can't read formulas. Maybe someone could explain what happens and why.
What you seem to be describing is the proper velocity or celerity, this is the same as velocity in Newton's theory but is not the same as velocity in relativity.

Perhaps a picture will help.

See below 'Einstein vs Newton'. While in Newton's theory a constant acceleration would pass the speed of light after 1 second (in this example) Einstein's theory changed all that. Think of it as some kind of law of 'diminished return" if your relative speed increases. The blue dotted line is the speed of light which I have set to 1. What you see here is a transformation from celerity to velocity.

Now can you see that the red line (Einstein) can never pass or even reach the one mark?

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#### pervect

Staff Emeritus
Relativity predicts these effects, and experiments confirm them. As far as "why" goes, one can try to explain why within the context of the theory of relativity, if that's what you're asking, but you'll have to learn some of the basics to follow the explanations. However, science can't answer the philosophical questions as to why relativity works - science is concerned with what works, what matches experiment. Relativity seems odd, but it matches experiment quite well.

As far as to "why" the universe is built that way, I would say, not entirely seriously if you want to know why it's built that way, for instance if you have some complaints, you'll have to find the creator and ask them. If they ever get out of committee meetings...

#### DaveC426913

Gold Member
As far as "why" goes,
I do not think he is asking the big why. He's asking the small why (call it the nitty gritty how).

He's simply having trouble understanding how constant thrust does not lead directly to constant acceleration. How going from v=0 to v=x will require a longer duration than going from v=x to v=2x. How v is asymptotic with c.

#### Darryl

The faster you go, the heavier you get, so it takes more and more energy to accellate you, your time also slows down, which means it takes longer time for you to expent the same amount of energy. So you get heavier and you have progressively less thrust because your time is taking longer.

So when your mass is infinite and your rate of time is zero, you just wont go anywhere, and you will stop accellerating, no matter how much energy you put into your engines.

If it takes a million year to put the same amount of fuel into your engine, as opposed to 1 second when you fist started, then you're thrust is that much less.

Combined with your massive mass you slow down to a crawl and the universe speeds up around you.

Not to mention to travel at a specific speed you have to 'throw out' stuff out the back at the same speed of faster than you want to travel.

If you cannot throw your stuff out the back at the speed of light or faster, you can never attain that speed.

Its like absolute zero, you might be able to get close, but you can never actually reach the true absence of heat from a body.

#### yuiop

There are many ways to calculate the speed of an object and in the cosmological context and in certain gravitational fields the speed of distant objects can appear to be greater than the speed of light and in certain oddball coordinates the speed of an object can appear to be greater than the speed of light, but two things are certain and clear:

1) Nothing with mass ever overtakes a photon.

2) Nothing with mass ever gets from A to B faster than a light signal travelling the same path.

#### DaveC426913

Gold Member
But not by myself. I see my OWN mass wrt myself to be constant regardless of where I am or at what speed I move. If I could take earth and my scale with me on a 0.9 C trip, I would weigh same on that scale.
Yes. Everything within your own frame of reference remains normal.

Now a question: in your own little bubble, how do you know that you are moving? How do you know whether you are travelling at .99mph or .99c?

A: By measuring the movement of things around you. Your movement is only relative to some other object(s), such as a nearby planet or the background of stars. This is the "relative" in relativity.

It is when you start measuring these other objects (their mass, their length contraction, their time dilation) that you realize your frame of reference is relativistically different.

And note, your FoR is only relativistically different as compared to other FoRs. There is no "real" or preferred FoR by which you can determine whether you are "really" moving.

#### TheTechNoir

By spacecraft's clock? Why? He is pushing constant G stilll.. Unless the universe expands and C is increasing (as predicted), there's nothing that I am aware of preventing the the guy in the spacecraft to reach C in the next second.

To the outside observer, yes. According to an external clock the speed will be .99999 then .9999999 etc etc., but I don't see the internal clock doing that.

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"here's nothing that I am aware of preventing the the guy in the spacecraft to reach C in the next second." .. unless the space flattening, as seen by the observer inside the ship is causing him to travel shorter distance with each second of his tick.
Bear in mind it is relative, there is no absolute speed in the universe. So we can only determine speed in respect to another perspective.

You are correct, to the perspective of the observer you are moving at .9999c, .99999c, etc.
You are wrong though, to the perspective of the internal clock - the traveller himself he is not traveling at the speed of light relative to his own local reference. If he were to shine a flashlight it would move ahead of him at the speed of light. And you can't think he just 'is' past the speed of light because again there is no absolute speed and to no observer including himself in the universe is he quite there.

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#### kamenjar

For mathematical details, see the following article about the "relativistic rocket":

http://www.phys.ncku.edu.tw/mirrors/physicsfaq/Relativity/SR/rocket.html [Broken]
Somewhere while browsing around this article, I found the answer, I guess...:

A controller based on Earth is monitoring a space ship moving away at a speed 0.8c. According to the theory of relativity, he will observe a time dilation that slows the ship's clocks by a factor of 5/3, even after he has taken into account the Doppler shift of signals coming from the space ship. If he works out the distance moved by the ship divided by the time elapsed as measured by the onboard clocks, he will get an answer of 4/3 c. He infers from this that the ship's occupants determine themselves to be traversing the distances between stars at speeds greater than the speed of light when measured with their clocks. From the point of view of the occupants their clocks undergo no slowing; rather, they maintain that it is the distance between the stars which has contracted by a factor of 5/3. So they also agree that they are covering the known distances between stars at 4/3 c.

Which to them appears as speed that is faster than however long the light would take in "rest" reference frame to reach. I didn't realize that you perceive this speed whenever you reach some significant relativistic speeds (there is some break-off). And of course, that doesn't mean that they would reach the star before the light would and see themselves taking off from earth, or that would pass the light from my flashlight inside the ship. It still though appears that there is still no relativistic barrier to you accelerating and continuing to accelerate at a rate that appears constant to you and "gaining speed continuously" with respect to distances measured in the earth reference frame.

May of you ask "what you mean by speed?" or "speed of light from where?". I guess I wasn't clear - the speed would be "static reference frame distance, over dilated time", which is in a way a wrong way to measure things, but still I guess a meaningful way.

You can just keep increasing that speed until you go nuts (if you could fuel) at what appears to you as a CONSTANT rate. And I was wrong to think that something significant happens at some break-off point, but there isn't one.

The reason I thought about it was the case when you leap towards a black hole. It looks similar to constantly accelerating ship. To an outside observer, you never reach the black hole. One would think that in your time frame you would simply fall into the event horizon, but even in this case you don't! The black hole evaporates before you reach it

In other words, each of you is in a way right, but you guys get too bogged down in perceiving speed from a "earth reference frame".

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#### Ich

That's http://en.wikipedia.org/wiki/Proper_velocity" [Broken].

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#### kamenjar

That's http://en.wikipedia.org/wiki/Proper_velocity" [Broken].
Man, I wish wikipedia articles were in english :)

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#### Passionflower

Here is a graph of a rocket traveling with a proper acceleration of 1 showing velocity, celerity and rapidity and the diminishing coordinate acceleration.

The area bounded by the Coordinate Acceleration is the velocity while the area bounded by the velocity is the total distance traveled. The rapidity (because the proper acceleration is 1) also shows the proper time for an observer in the rocket.

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#### kamenjar

A graph to show velocity, celerity and rapidity and to show the diminished coordinate acceleration while the proper acceleration remains constant:

View attachment 28923
So then celerity is perceived (proper?) speed/acceleration from the moving reference frame of the object that is traveling, considering that object's clock?

#### Passionflower

So then celerity is perceived (proper?) speed/acceleration from the moving reference frame of the object that is traveling, considering that object's clock?
Celerity is basically chart velocity. Ignoring acceleration to keep it simple, suppose you want to go to a far a way planet. You check the latest edition of Google SpaceCharts and see it is 1 light year away. Say you want to get there in half a year, then the rocket must travel with a celerity of 1/0.5= 2

Then with a celerity w=2 the rocket's velocity would be:

$${w \over \sqrt{1+w^2}} = 0.8944271908$$

The rapidity would be:

$$ln(w+ \sqrt{1+w^2}) = 1.443635475$$

On arrival the clock at home would read:

$${1 \over v} = 1.118033989$$

An observer on earth watching through a telescope would see your clock during travel slowed down by a factor of:

$${w + \sqrt{1+w^2}} = 4.236067977$$

While, if he takes into account the finite speed of light, he would conclude your clock is slower by a factor:

$$\sqrt{1+w^2} = 2.236067976$$

As you can see simply the Doppler factor minus the celerity.

As you can see, starting from celerity the formulas as easy to remember the recurring part is

$$\gamma = \sqrt{1+w^2}$$

Which is sometimes called the Lorentz factor.

How do you add two celerities together? Just multiply the Doppler factors!

Now of course it is simple if all the motion is one dimensional, when we get tree dimensional motion it becomes far more complicated, unfortunately I cannot find anything in the literature giving a comprehensive description of celerity in three dimensions and all the relevant formulas. If someone knows, please let me know where we can find this.

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#### TheTechNoir

Somewhere while browsing around this article, I found the answer, I guess...:

A controller based on Earth is monitoring a space ship moving away at a speed 0.8c. According to the theory of relativity, he will observe a time dilation that slows the ship's clocks by a factor of 5/3, even after he has taken into account the Doppler shift of signals coming from the space ship. If he works out the distance moved by the ship divided by the time elapsed as measured by the onboard clocks, he will get an answer of 4/3 c. He infers from this that the ship's occupants determine themselves to be traversing the distances between stars at speeds greater than the speed of light when measured with their clocks. From the point of view of the occupants their clocks undergo no slowing; rather, they maintain that it is the distance between the stars which has contracted by a factor of 5/3. So they also agree that they are covering the known distances between stars at 4/3 c.

Which to them appears as speed that is faster than however long the light would take in "rest" reference frame to reach. I didn't realize that you perceive this speed whenever you reach some significant relativistic speeds (there is some break-off). And of course, that doesn't mean that they would reach the star before the light would and see themselves taking off from earth, or that would pass the light from my flashlight inside the ship. It still though appears that there is still no relativistic barrier to you accelerating and continuing to accelerate at a rate that appears constant to you and "gaining speed continuously" with respect to distances measured in the earth reference frame.

May of you ask "what you mean by speed?" or "speed of light from where?". I guess I wasn't clear - the speed would be "static reference frame distance, over dilated time", which is in a way a wrong way to measure things, but still I guess a meaningful way.

You can just keep increasing that speed until you go nuts (if you could fuel) at what appears to you as a CONSTANT rate. And I was wrong to think that something significant happens at some break-off point, but there isn't one.

The reason I thought about it was the case when you leap towards a black hole. It looks similar to constantly accelerating ship. To an outside observer, you never reach the black hole. One would think that in your time frame you would simply fall into the event horizon, but even in this case you don't! The black hole evaporates before you reach it

In other words, each of you is in a way right, but you guys get too bogged down in perceiving speed from a "earth reference frame".
I believe I am completely understanding your thought process behind this perspective.

You are thinking if you hypothetically continue accelerating to arbitrary velocities, then while relativistic effects prevent you from surpassing the speed of light surely in your OWN frame of reference if you hypothetically continued accelerating for an infinite amount of time lets say, then it would be inevitable that from your own frame of reference you have indeed broken the light barrier. You are also acknowledging and understanding that if you shine a flashlight even after you have passed the light barrier it will still shine ahead of you at the speed of light. So while you are not technically past the speed of light in your frame of reference, you have in some other way still actually achieved light speed as you have been accelerating consistently for up to an infinite amount of time. No?

The problem with this mentality though is that if you were to hypothetically continue said acceleration you still are always only accelerating in reference to something else, again there is no fixed space in which you are moving across faster and faster. So for you, you will never even approach light speed because light will never slow down for you. So from your perspective this acceleration will have relativistic effects on external things you observe but never directly effect you personally. Whereas from any other observers perspective, as you continue accelerating you get closer and closer but you never reach light speed as the acceleration slows more and more. This is all that matters, what you experience (no light speed) and what others experience (they see you traveling at less than c) there is no being immune to relativity that can observe you accelerating at a defined/fixed/true consistent speed until you eventually surpass c.

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