# Why can't light travel faster than c?

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Aarav
Photons do not have mass, so why stop at 299700 km/s??

Mentor
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As with all "Why" questions, there is not really an answer:

Tolklein and Aarav
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Because they do.

There are only two systems of physics consistent with the principle of relativity, Newtonian physics and relativity. Both have an invariant speed - infinite speed in Newtonian physics and some finite value in relativity. The value of that finite speed is whatever we define it to be - it depends on our unit choice.

The values that we can't choose are dimensionless numbers like the fine structure constant.

Aarav
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Photons do not have mass, so why stop at 299700 km/s??

Light is electromagnetic radiation, hence obeys Maxwell's equation and moves at a single speed. It can't move at any other speed.

Aarav
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Heh - three answers, three completely different approaches...

Aarav and russ_watters
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Heh - three answers, three completely different approaches...
Yeah, a bit mathematical: all right and none answers the question!

DanielMB and Aarav
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Yeah, a bit mathematical: all right and none answers the question!
They all answer bits of it. I have no idea how long a complete answer would be...

Staff Emeritus
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I am with Feynman on this one.

Describing "why" is not the aim of physics as an empirical science. Of course we can model things and start explaining why something is so and so according to the model, but it will not answer the "deeper" question. There does not have to be a deep "why" in Nature's behaviour. The "why" is just attached to our models and theories.

You can say that it is because light satisfies Maxwell's equations or you can say it is because it is the only thing compatible with the principle of relativity, but that just translates the question to why Maxwell's equations are a good description of nature or why the principle of relativity should hold.

Sean Nelson, bhobba and Aarav
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Sean Nelson, Aarav and bhobba
itfitmewelltoo
All physics theory has a point at which no further explanation can be had. Physics (and all knowledge) is, at it's core, simply a demonstration of correlations. If I flip the light switch then the light goes on. The state of the light is correlated with the state of the switch. The state of the switch and light correlate with the measurement of current which correlates with the digits on my multimeter. A broken wire correlates with the switch not correlating with the light. And on and on we go until there are no further observations of things that can be had. All that exists has been observed.

Physics shows how things occur. The answer to "why" is simply "because".

Aarav
Outhouse
All physics theory has a point at which no further explanation can be had.

No advancements would ever be made without the curiosity to explain what no one has as of yet.

Sean Nelson and Aarav
Outhouse
Describing "why" is not the aim of physics as an empirical science.

While true science does not prove anything, it observes and reports. People can use said information to make plausible assumptions to the point of factual knowledge.

Why is the question that drives knowledge to expand.

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No advancements would ever be made without the curiosity to explain what no one has as of yet.
True but that does not in any way invalidate the post to which you responded.

Aarav
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Please stay on topic. No dark matter or energy (content of deleted off topic posts) is needed here.

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bhobba
Fig Neutron
Everyone please correct me if I’m wrong, but this is how my tenth grade physics book explained it. If something went faster than the speed of light it would have a negative length and an infinite mass. This was probably simplified significantly but it made sense to me.

Mentor
It's dangerous to use a 10th grade Physics book to understand advanced physics.

Years ago the atom was described as being like a miniature solar system in elementary science books in the 50's and 60's despite quantum mechanics saying that's an incorrect and wrong way to look at it.

Relativity is based on the notion that the speed of light is the maximum an object with mass can travel. It's a barrier that we can't breach.

Things like Alcubierre drive use schemes of distorting spacetime using exotic matter to transport something faster than light. However, exotic matter is something we have yet to discover.

https://en.wikipedia.org/wiki/Alcubierre_drive

2022 Award
Everyone please correct me if I’m wrong, but this is how my tenth grade physics book explained it. If something went faster than the speed of light it would have a negative length and an infinite mass. This was probably simplified significantly but it made sense to me.
No. In modern terminology, mass refers to the invariant mass, which doesn't increase. You are referring to the relativistic mass, which is basically a confusing name for energy. This does tend to infinity as the velocity of a massive object approaches c, but a massive object cannot reach or exceed c.

It's not really an explanation for why you can't exceed c, because the first line in the derivation of relativistic energy is basically an assumption that you can't exceed c.

"Because when we assume you can't exceed c we make correct predictions" is really the best we can do.

fresh_42
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Photons do not have mass, so why stop at 299700 km/s??

Basically its because if you have a look at the symmetry of the situation - and it requires math above B level - but I will post it anyway - it shows there is a maximum velocity things can travel at (it may be infinity):
http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

Experiment shows its finite and not infinity - that's just how nature is. Here is a simple reason why. One of the consequences of their being a finite velocity is length shortening of moving bodies. Suppose you have a positive current traveling in one direction and the same amount of negative current traveling in the opposite direction. They are contracted equally so have exactly the same charge density so for you the electric field is zero and and charges you have at rest will feel no electrical force. Now suppose the charge starts to more - for it then one current is larger than the other and the charge density is no longer the same for both currents because they are moving at different velocities so experience different amounts of contraction. This leads to an electric field being present on that charge, so if length contraction is happening and because of a maximum speed we have a prediction. Do we know what that situation is?. Of course we do - its interpreted as a moving charge in a wire having a magnetic field. The very existence of magnetism, electric motors and a massive amount of our electrical technology is due to the fact there is a maximum speed. It turns out to be the speed of light.

In fact, and again this is beyond the B level, and unfortunately can't be explained at that level, Maxwell's equations can be derived from Coulomb's force law you probably have heard of and that maximum speed is the speed of light:

It is even possible by assuming nothing but relativity and making a few assumptions (some they hide from you - naughty naughty) to derive Maxwell's equations from that maximum speed being the speed pf light:
http://iopscience.iop.org/article/10.1088/0143-0807/36/6/065036/pdf

All this is basically saying is we have many ways to determine that the maximum speed things can travel is the speed of light. But asking why? The answer is, as far as we can tell today,and I know its a bummer, simply because its how nature is.

Thanks
Bill

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Mentor
No advancements would ever be made without the curiosity to explain what no one has as of yet.

But what if nature does not oblige and it is a fundamental law not derivable from other laws or logically equivalent laws? As an example, you may consider the following an explanation, but it really is just a logically equivalent law saying the same thing - it is the speed of a source that emits light does not have any effect on the speed of light. This follows from both experiment and the theory of Electromagnetism. So it doesn't matter how fast you travel the speed of light is the same because the only difference is the speed of the source - but that does not affect the speed of light. You may think you have given an explanation of the constancy of the speed of light - but really you haven't - all you have done is state it in different language - the two are logically equivalent. Physicists for over a century now have tried, and failed to find a reason.

Just because you want it does not mean it's there. And of course we have people looking - but so far have come up empty.

Nature is as nature is - do not fight it - simply accept it - if there is a deeper answer its OK to look for it - if not that's OK as well. We each must decide what is worthwhile for us to investigate.

As usual Feynman states it clearly and succinctly:

Thanks
Bill

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fresh_42
Mentor
Everyone please correct me if I’m wrong, but this is how my tenth grade physics book explained it. If something went faster than the speed of light it would have a negative length and an infinite mass. This was probably simplified significantly but it made sense to me.
That is a very unfortunate explanation. It is true that if you plug a speed greater than ##c## into some of the equations of special relativity you will get an impossible (not negative, but something worse - the square root of a negative number) length and mass (actually energy, but that's a longer digression). However, those equations are derived from assumptions that are equivalent to saying that no object can go faster than light so they cannot describe something moving faster than light; the absurd result is just telling you that you're trying to use the equations under conditions where they don't apply.

Dr Whom, Sean Nelson, DanielMB and 3 others
Outhouse
But what if nature does not oblige and it is a fundamental law not derivable from other laws or logically equivalent laws?

Much of the nature of our universe falls in a place without current laws or knowledge, many things we have had certainty on, have been overturned with new discoveries.

We are at the infancy of our understanding the nature of space/time and gravity.

I think it was Einstein that quoted he was just more curious then many of his peers.

So to answer your question directly, I would say one needs to keep an open mind while choosing his battles wisely. There are many holes that need to be filled at this time.

Take OPs question. For me, the speed of a race car is determined by track conditions, and we cannot even define the fabric of space properly.

weirdoguy
and we cannot even define the fabric of space properly.

Maybe because there is no "fabric of space"...

PeroK, Sorcerer, phinds and 1 other person
Outhouse
True but that does not in any way invalidate the post to which you responded.

Do all physics theory's complete our understanding of the nature in the universe? or are we trying to advance the theory's?

Mentor
That is a very unfortunate explanation.

Indeed it is .

Here is a much better one and based on one of the foundational principles of physics called the principle of relativity (POR). Its so simple a 10th grader can understand it yet so profound it is the base of much of modern physics.

First of all you need to know what an inertial frame is. A frame is a conventional standard of rest experiments can be done on. An inertial frame is a frame such that all points, times, and directions are equivalent - as an aside that already has profound consequences from something called Noethers Theorem I will leave those reading this look up - we don't totally hold peoples hand around here. The POR states the laws of physics are the same in all inertial frames or frames moving at constant velocity wrt to an inertial frame. It can also be shown any two inertial frames must move at constant velocity wrt to each other.

We have the main concept out of the way. We know the speed of light does not depend on the speed of the source. So it doesn't matter what inertial frame you are in a beam of light will always travel at the same speed. You try to catch up to it - and it keeps moving away from you at the speed of light. To someone watching you try to do it they will say you can never catch it - hence can never even reach the speed of light - little alone catch up to it or exceed it. Wheeler, Feynman's PhD adviser (just thought I would throw that one in, in the hope it may pique someones interest) expresses it this way - forward is always forward.

Thanks
Bill

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Fig Neutron
Mentor
and we cannot even define the fabric of space properly.

Did you study Euclidean geometry? Was that a fabric?

But this is getting way off topic - so please nothing more on personal conjectures such as space is a fabric - we simply do not know.

Thanks
Bill

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Gold Member
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Do all physics theory's complete our understanding of the nature in the universe? or are we trying to advance the theory's?
I'm not aware of ANYTHING that "completes" our understanding of the nature in the universe but science extends our understanding of parts of it. I have no idea what you mean by "or are we trying to advance the theory's?"

Helios
The OP's question is answered by supposing it is true and then showing a contradiction. If light could travel faster than c, we could build a scope to see things happen earlier than when one could have otherwise seen them. So we could make a prophecy scope, and this is a supernatural device, good for Harry Potter, but not a physics discourse.

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The OP's question is answered by supposing it is true and then showing a contradiction. If light could travel faster than c, we could build a scope to see things happen earlier than when one could have otherwise seen them.
However, here you're making the hidden assumption, that information transmission is limited by ##c## whereas light is not. This is a circular reasoning and thus no proof: If light was faster than ##c## and we can see only as fast as ##c## then this is a contradiction.
So we could make a prophecy scope, and this is a supernatural device, good for Harry Potter, but not a physics discourse.
With this kind of reason you can prove everything, even the opposite.

bhobba
Helios
If light could be made to go faster than c'>cc and we can only ever see as fast as c'>cc, is a contradiction. What I said.

2022 Award
If light could be made to go faster than c'>cc and we can only ever see as fast as c'>cc, is a contradiction. What I said.
But how could we only "see at c'" if light went faster than that? We see using light. That's the point @fresh_42 is making.

Helios
We see using light.

Thanks.

LitleBang
A clock on the moon runs faster than than a clock on earth. Wouldn't the speed of light measured on the moon be slower than measured on the earth?

weirdoguy
A clock on the moon runs faster than than a clock on earth.

No, it runs 1 second per second, just as every other clock.

Dale
Mentor
A clock on the moon runs faster than than a clock on earth.

As @weirdoguy has pointed out, this is not the right way to think about it--particularly as putting it this way has led you to the incorrect inference that the measured speed of light on the moon might differ from that on earth.

The correct way to put it is that, if we have observers on the moon and the Earth who are exchanging round-trip light signals, the round-trip light travel time will be less by the Earth observer's clock than it is by the moon observer's clock. But this is not a measurement of the speed of light. Either observer can set up a local experiment to measure the speed of light (for example, reflecting a round-trip light signal from a mirror at known fixed distance away from him), and both of them will measure the same result.