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

• engi2013
In summary: Basically, light travels at the speed of causality because it is massless. This can be derived from quantum electrodynamics. If an object with mass were to travel at the speed of light, it would require infinite energy to accelerate it. This is because the work required to accelerate an object to the speed of light approaches infinity as the speed approaches c. This also means that it is not possible for an object with mass to travel faster than the speed of light. If such an object were to hypothetically exist, it would have to have some very strange properties.
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.

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.

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).

engi2013 said:
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 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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engi2013 said:
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.

engi2013 said:
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.

bcrowell said:
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 ?

heldervelez said:
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.

Fredrik said:
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?

heldervelez said:
Fredrik, OK.
https://www.physicsforums.com/showpost.php?p=2484840&postcount=82" I've expended some words that adds to the subject.
The OP are similar.

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?

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cfrogue said:

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 preferred 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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heldervelez said:
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.

bcrowell said:
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.

engi2013 said:
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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engi2013 said:
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.

Nickelodeon said:
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.

espen180 said:
Nickelodeon said:
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.

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.

Al68 said:
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.

DarkStar7 said:
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.

pliu123123 said:
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.
Both of these are simply non-sense. The fact that no massive body can move faster than light has nothing at all to do with whether or not we "observe" the universe through light. That leads to silliness like someone arguing here, a few years back, that, to a blind person, nothing can move faster than sound!

HallsofIvy said:
Al68 said:
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.
That's not in a third reference frame like I specified, that's the speed of one rocket in the rest frame of the other. That's why I specified "in a third reference frame", or "launch" frame. The separation speed of the rockets in the launch frame is 1.8c. In the launch frame, the distance between the rockets is increasing 1.8 light years per year.

I think that was Nickelodeon's intended meaning, although it wasn't worded that precisely.

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HallsofIvy said:
Both of these are simply non-sense. The fact that no massive body can move faster than light has nothing at all to do with whether or not we "observe" the universe through light. That leads to silliness like someone arguing here, a few years back, that, to a blind person, nothing can move faster than sound!

but did people in the past conveniently do experiments in dark?

Information transfer delay is corrected for in the equations of relativity. Even if you could see events instantaneously, the effects predicted by relativity would still prevail.

Also, it is false to assume that hypothetical objects traveling faster than c would be invisible to us. However, it would produce some weird effects, for example a body traveling towards you would appear to travel away from you.

HallsofIvy said:
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.

I think you should have said "observed speed relative to each other". The measurement of the relative speed you are talking about is subject to the limitations of the data carrier.

This following text is not mine but illustrates quite well what I'm trying to get across

"Imagine this situation: Spaceship A is 1 light year to the west of me and travels at a speed of 0.9999c towards me; Spaceship B is 1 light year to the east of me and travels at a speed of 0.9999c towards me. What's their distance apart according to me? 2 light-years. When do they reach me? In about 1 year. So the separation distance decreases at a rate of about 2c according to me."

The post goes on to acknowledge "Of course the relative speed of spaceship B as measured by spaceship A is still less than c."

Hope that clears things up
Nick

If you assume an object can move faster than light you can have some fun using spacetime diagrams. You can show that you would not see the superluminal object until it was alongside you and then you would see a future going image of the object going away from you and another image of the object going away from you, but in the opposite direction and going backwards in time. You can also show that two snipers using conventional weapons and aiming in opposite directions would both score direct hits on the superluminal target if they fire their weapons simultaneously. (It would have to be a lucky shot or the trajectory of the superluminal target would have to be prearranged, because of course they can not see the target before they fire.) In other threads it also been demonstrated that with superluminal transfer of objects or information you can have the ansers to your questions before you have even asked the question. I am sure there is lot more fun and paradoxes to be had, once you assume superluminal travel. Basically the universe stops behaving in a sensible way.

Also, you get complex quantities from the time dilation and length contraction quantities.

Let's say we travel at 2c relative to an observer. The LC formula gives $$l=l_0\sqrt{-1}=l_0i$$. The TD formula gives $$t=\frac{t_0}{i}=-t_0i$$.

Notice the negative time.

espen180 said:
Also, you get complex quantities from the time dilation and length contraction quantities.

Let's say we travel at 2c relative to an observer. The LC formula gives $$l=l_0\sqrt{-1}=l_0i$$. The TD formula gives $$t=\frac{t_0}{i}=-t_0i$$.

Notice the negative time.

The negative time issue is no big deal. It just means, as an observer you would see events prior to the initiation of the event from which you began taking your time measurements - naturally so. It doesn't mean time is traveling backwards, it just means the data that you are reading is older than your current time less the relative time it has taken for the data from a specific event to reach you.

## Why is the speed of light considered to be the universal speed limit?

According to Einstein's theory of relativity, the speed of light is considered to be the maximum speed at which anything in the universe can travel. This is because as an object approaches the speed of light, its mass increases infinitely and requires an infinite amount of energy to accelerate further. Therefore, it is physically impossible for any object to reach or exceed the speed of light.

## How is the speed of light measured?

The speed of light is measured in a vacuum, where it travels at a constant speed of approximately 299,792,458 meters per second. This measurement is based on the distance light travels in one second, which is defined as the length of time it takes for light to travel 299,792,458 meters.

## Can anything travel faster than the speed of light?

No, according to our current understanding of physics, nothing can travel faster than the speed of light. This includes all forms of matter, energy, and information.

## Why is it important to understand the speed of light?

Understanding the speed of light is crucial in many areas of science, such as astronomy, telecommunications, and particle physics. It allows us to accurately measure distances in the universe and communicate over vast distances. Additionally, it is a fundamental constant that helps shape our understanding of the laws of physics.

## Could our understanding of the speed of light change in the future?

While our current understanding of the speed of light is based on Einstein's theory of relativity, it is always possible that new discoveries and advancements in science could lead to a better understanding of this fundamental constant. However, based on our current knowledge, it is highly unlikely that the speed of light will ever be surpassed.

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