# Seriously, why can't I go faster than the speed of light?

#### engi2013

What makes light so special? Are they basically saying I can't go faster than electromagnetic waves in general? Why not? Since when did they decide our universe? Hypothetically speaking, what if I did go faster than the speed of light? Would the universe explode or something? Is this just proven mathematically, like how you can't divide by zero? Give me intuitive answers with cool examples please.

#### Dmitry67

Yes, the closest thing is 'divide by zero'
You can also thing about c as infinity. It is finite (300000km/s), but in some sense it is infinity in psedo-euclidean spacetime.

#### Fredrik

Staff Emeritus
Gold Member
The work you need to perform to accelerate a mass m to velocity v goes to infinity as v goes to c. (The calculation is here). Because of that, it doesn't make sense to ask what would happen if you travel faster.

So is there something that can? Possibly, but not likely. Matter that moves faster than c would have to have some really weird properties. In particular, it can't have mass m>0. Instead it would satisfy m2<0. (Yes, really). The reason involves both quantum mechanics and some advanced mathematics (finding all irreducible representations of the Poincaré group). This stuff would have to have some even weirder properties in order to avoid paradoxes. See my posts in this thread, in particular #17 and #24, and keep in mind that time is in the "up" direction in the diagrams I'm talking about, and that coordinates of events are written with the time coordinate first (t,x). Note however that you need a very solid understanding of simultaneity in SR to really understand this.

The reason why light travels at the invariant speed is that photons are massless. This is something that can be derived in quantum electrodynamics. (By "this" I mean their speed, not their mass. The fact that they are massless is part of what we mean by a photon).

#### bcrowell

Staff Emeritus
Gold Member
What makes light so special? Are they basically saying I can't go faster than electromagnetic waves in general? Why not? Since when did they decide our universe? Hypothetically speaking, what if I did go faster than the speed of light? Would the universe explode or something? Is this just proven mathematically, like how you can't divide by zero? Give me intuitive answers with cool examples please.
There is nothing special about light. c isn't the speed of light, it's the maximum speed of cause and effect. Light just happens to travel at c.

For an explanation of why there is a maximum cause of speed and effect, see this link: http://www.lightandmatter.com/html_books/6mr/ch01/ch01.html [Broken] It follows from the observed properties of spacetime: causality, symmetry, and nonsimultaneity. For a more formal and mathematical treatment, see Rindler, Essential Relativity: Special, General, and Cosmological,
Springer-Verlag, 2nd ed., 1977, p. 51

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#### DarkStar7

What makes light so special? Are they basically saying I can't go faster than electromagnetic waves in general? Why not? Since when did they decide our universe? Hypothetically speaking, what if I did go faster than the speed of light? Would the universe explode or something? Is this just proven mathematically, like how you can't divide by zero? Give me intuitive answers with cool examples please.
Most people don't understand the basic concept of the speed of light. Basically it's related to our own perspective. It should be stated that you can't perceive something going faster than the speed of light.
No matter how you move in uniform motion, ie not feelling g forces you can argue that you are at rest and measure another objects speed relative to yourself. Believe it or not, if you were to constantly accellerate, feeling say a couple of g per second..you can accellerate forever! Think about it!

Imagine your in the middle of the pacific ocean in a little rowing boat, and imagine the horizon represents the speed of light. No matter how fast you row towards that horizon it will always maintain the same distance away from you.
Other peoples perspective of the horizon in their rowing boats will differ from yours, but their measure the distance to the horizon (the speed of light) will always remain the same...whereever they are. The horizon is centered on you and moves with you, and in the same way your perception of the speed of light is centred on you.

#### cfrogue

What makes light so special? Are they basically saying I can't go faster than electromagnetic waves in general? Why not? Since when did they decide our universe? Hypothetically speaking, what if I did go faster than the speed of light? Would the universe explode or something? Is this just proven mathematically, like how you can't divide by zero? Give me intuitive answers with cool examples please.
Yes in a way, the equation used for special relativity to decide time dilation and length contraction is

1/ sqrt( 1 - v²/c² )

And more specifically,

t' = t * sqrt( 1 - v²/c² )

This would mean time would exist in the complex number system which makes no sense.

This means you take the square root of a negative number.

#### heldervelez

There is nothing special about light. c isn't the speed of light, it's the maximum speed of cause and effect. Light just happens to travel at c.
...

Light is energy. Energy is exchanged at most at light speed 'c'.
And light speed 'c' because space (or any other medium where light travels) says so.
The 'c' is the maximum speed of cause and effect' is consequence and not the cause.
Then 'Light just happens to travel at c' is not correct.

Another question is about the energy budget. How much energy must be used to accelerate an object of mass > 0 (rest mass) until it reaches 'c' ? The whole energy available on the universe ?

#### Fredrik

Staff Emeritus
Gold Member
Another question is about the energy budget. How much energy must be used to accelerate an object of mass > 0 (rest mass) until it reaches 'c' ? The whole energy available on the universe ?
That won't be sufficient. See #3 and the post I linked to there.

#### heldervelez

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#### espen180

The reason why light travels at the invariant speed is that photons are massless. This is something that can be derived in quantum electrodynamics.
Do you really need quantum electrodynamics for this? Classical electrodynamics gives the same result. Even though the model has its limitations, doesn't it seems rigid in this area?

#### cfrogue

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#### heldervelez

The permeability and the permittivity (and 'c') are 'properties' of space (or medium) that dictates the rate of change of energy transfers (and information exchange).

Is this the frame space or some global space?
It is the absolute essence of universe (in this sense we can be a bit philosophical, and who knows if in some future theory the 'space' becames the fundamental 'substance' that embodies every aspect of the reality (like Spinoza, dutch philosopher of portuguese jewish origin).

It's the 'stage' (my prefered figurative name) also known as vacuum, medium, vacuum space, aether,
add mass but it does not remove the space, add radiation but it does not remove the space, add field but it does not remove the space, add 'particles' but it does not remove the space.
The permeability and the permittivity are 'properties' of space and change dependent on the content. 'c' depends on those two properties by that equation.
I mencioned the Bose-Einstein condensate as an extreme situation where photons are constrained to such a drastic slow down ( http://en.wikipedia.org/wiki/Speed_of_light#Propagation_of_light").
Then 'c' is not an absolute 'constant' ?
The answer must be yes, but its value varies dependent on the properties of the 'stage'.

Can you elaborate on 'frame space' ? I'm not sure if I understood your doubt.

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#### bcrowell

Staff Emeritus
Gold Member
Light is energy. Energy is exchanged at most at light speed 'c'.
And light speed 'c' because space (or any other medium where light travels) says so.
The 'c' is the maximum speed of cause and effect' is consequence and not the cause.
Then 'Light just happens to travel at c' is not correct.
It's actually possible to do the logical framework in either way. (1) If you assume the speed of light is universal, you can prove that simultaneity is observer-dependent and that c is the maximum speed of cause and effect. (2) If you assume that simultaneity is observer-dependent, then you can prove that there is a maximum speed of cause and effect, and that light travels at that speed. See Rindler, Essential Relativity: Special, General, and Cosmological, Springer-Verlag, 2nd ed., 1977. He does the reasoning first according to #1 above, and then redoes it on p. 51 according to #2, which explicitly shows that either way is logically complete and self-consistent. Approach #1 is older, and more people are familiar with it. Approach #2 is more in keeping with the modern way of thinking about spacetime.

#### heldervelez

It's actually possible to do the logical framework in either way. (1) If you assume the speed of light is universal, you can prove that simultaneity is observer-dependent and that c is the maximum speed of cause and effect. (2) If you assume that simultaneity is observer-dependent, then you can prove that there is a maximum speed of cause and effect, and that light travels at that speed. See Rindler, Essential Relativity: Special, General, and Cosmological, Springer-Verlag, 2nd ed., 1977. He does the reasoning first according to #1 above, and then redoes it on p. 51 according to #2, which explicitly shows that either way is logically complete and self-consistent. Approach #1 is older, and more people are familiar with it. Approach #2 is more in keeping with the modern way of thinking about spacetime.
In the real world both formalisms are similar.
The 'simultaneity' is chosen by convention, as Einstein did, but there may be other methods.
For example, an observer with 'instant vision' (not real and not actuating) has a different notion of simultaneity and yet could understand everything that the other observers (actuating ones) had measured. That is, with this special observer neither hypothesis 1 nor 2 are consistent.
I accept the equivalence of both forms.

#### pliu123123

What makes light so special? Are they basically saying I can't go faster than electromagnetic waves in general? Why not? Since when did they decide our universe? Hypothetically speaking, what if I did go faster than the speed of light? Would the universe explode or something? Is this just proven mathematically, like how you can't divide by zero? Give me intuitive answers with cool examples please.
Ya,a simple approach is that because we use light to observe this amazing world, all the speed we detect or sense or describe should not be greater than that of light~

just like if we want to take a bath in the bathtub, our body size should not be greater than it.

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#### Nickelodeon

What makes light so special? Are they basically saying I can't go faster than electromagnetic waves in general? Why not? Since when did they decide our universe? Hypothetically speaking, what if I did go faster than the speed of light? Would the universe explode or something? Is this just proven mathematically, like how you can't divide by zero? Give me intuitive answers with cool examples please.
Under normal conditions you can't go faster than c. However you can have a real speed of separation (or convergence) from another object at 2c.

#### espen180

Under normal conditions you can't go faster than c. However you can have a real speed of separation (or convergence) from another object at 2c.
Not from your own reference frame. You can never measure yourself to move relative to anything else with a speed larger than c.

A

#### Al68

##### Guest
Under normal conditions you can't go faster than c. However you can have a real speed of separation (or convergence) from another object at 2c.
Not from your own reference frame. You can never measure yourself to move relative to anything else with a speed larger than c.
I think Nickelodeon meant the relative velocity between two objects was limited to 2c in a third reference frame. Like two rockets launched in opposite directions as measured by an observer on earth.

#### espen180

In any case, "real" speed is ambigous. The speed I measure is as real to me as the speed you measure is to you. You have to specify from which frame the measurement is made in order to make sense of an argument.

#### HallsofIvy

I think Nickelodeon meant the relative velocity between two objects was limited to 2c in a third reference frame. Like two rockets launched in opposite directions as measured by an observer on earth.
No, that's still wrong. If two rockets were launched in opposite directions with speed .9c relative to an observer on earth, their speed relative to each other would be
$$\frac{.9c+ .9c}{1+ \frac{(.9c)(.9c)}{c^2}}= 0.9945c$$
approximately.

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