Need help explaining light speed limit to younger brother

In summary, the conversation discusses the concept of traveling faster than the speed of light and whether it is possible or not. The participants touch on topics such as E=MC2, the limitations of mass and energy, and the theories behind the speed of light being the maximum speed in our universe. They also discuss the idea of acceleration and time dilation in relation to surpassing the speed of light. Ultimately, the conversation concludes that it is not possible to physically exceed the speed of light due to the limitations of mass and energy.
  • #1
MasterZoran
1
0
Hi everyone - I am having trouble getting my brother to wrap his head around why you cannot move faster than the speed of light.

My little brother has said that he believes eventually we will have technology that will allow FTL travel - I agree with this but I told him that IF it happens it will not be because of us literally moving FTL, it will be because we figure out how to bend space to allow us to cover great distances in a short time (think of the ant and the thread, then folding the thread - this is how I believe FTL travel *may* work)

I tried to explain to him E=MC2 and diminishing returns - how the more energy you put into an object the more mass it has, so even if you could come up with an "infinite" energy supply and were to pour "infinite" amount of energy into an object the object's mass would increase proportionately with diminishing returns so you would never actually reach light speed -

he seems to think that eventually - some day we will overcome this limit - I told him the universe would probably break

can anyone link me to a good article or help me come up with some way to explain why light speed is a hard limit - why it cannot ever be exceeded by objects with mass

-ps, I'm sure many of the terms / ideas I am using are not perfectly accurate - I'm just generalizing some advanced concepts for the sake of explanation based on my limited understanding of special relativity - I am no scientist

I might even be the one who is wrong - but I would love to learn why/why not.

thanks!

Edit: The gist of what I am getting at is in the definition of "Traveling faster than light speed" - If you define it as moving from one place to another quicker than light would get there I do believe that possible.

If you define it as accelerating too and past the speed of light I believe that is not possible, now or ever
 
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  • #2
If your question is "why can an object with mass physically not exceed the speed of light", I think you have already answered it. It would take an infinite amount of energy.

If your asking "Why is the speed of light the limitation that it is in our world", as opposed to, "why the limitation is not one mile-an-hour faster", I'm not sure anyone can answer that one yet, at least I have not read a good answer.

I have read one theory as to why there has to be some type of limitation (as opposed to no limit) on movement through space. If I understood the explanation correctly, it is because time is (according to this theory) like a concatenation of individual "moments" - similar to a motion picture. And this speed limitation (light speed) determines the maximum amount of difference there can be between the individual "frames" of time. Otherwise, time would not appear to us to flow smoothly, and would appear erratic. It made sense to me, at least.

Daisey
 
  • #4
map19 said:
But if you have a spaceship with an engine capable of providing, say 5g for a very long time, you would, by your own calculation, reach and surpass the speed of light referred back to the take-off.

No, you won't. It is very easy to disprove your statement:

[tex]v=\frac{at}{\sqrt{1+(at/c)^2}}[/tex]

Calculate [tex]v[/tex] for [tex]t->oo[/tex].
 
  • #5
starthaus. You haven't disproved anything.
you are referring back to the start point or reference frame because these relativistic formulae always do.
If you are inside a ship and it accelerates at a constant rate, eventually, by your own calc of constant speed increase x time you will see that you have exceeded c.
Observers in other frames will see that you get ever closer, but never reach c.

Where's my post gone ?
 
  • #6
map19 said:
starthaus. You haven't disproved anything.
you are referring back to the start point or reference frame because these relativistic formulae always do.
If you are inside a ship and it accelerates at a constant rate, eventually, by your own calc of constant speed increase x time you will see that you have exceeded c.

You must be reading too much sci-fi.

Observers in other frames will see that you get ever closer, but never reach c.

which means precisely that the ship will NEVER reach c.

Another way of proving that is by obeserving that the mechanical work necessary to get to [tex]v=c[/tex] starting from [tex]v=v_0[/tex] is:

[tex]\Delta W= m_0c^2(\gamma(v=c)-\gamma(v=v_0))=oo[/tex]
 
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  • #7
map19 said:
starthaus. You haven't disproved anything.
you are referring back to the start point or reference frame because these relativistic formulae always do.
If you are inside a ship and it accelerates at a constant rate, eventually, by your own calc of constant speed increase x time you will see that you have exceeded c.
Observers in other frames will see that you get ever closer, but never reach c.

So what is your calculated superluminal speed relative to?

Matheinste.
 
  • #8
I'm not going to do the math here...but let's say you DO accelerate at 5g for 20 or so years, and then slow down at 5g for another 20 years. You'd probably end up at the other end of the universe...if not beyond it. You then look back at the distance you covered, and look down at your watch/ calendar...wouldn't YOU be able to say, with a clear conscience, that you WERE traveling faster than the speed of light? (I understand that millions/ billions of years will have passed for the universe, but bear with me here...)
 
  • #9
map19 said:
starthaus. You haven't disproved anything.
you are referring back to the start point or reference frame because these relativistic formulae always do.
If you are inside a ship and it accelerates at a constant rate, eventually, by your own calc of constant speed increase x time you will see that you have exceeded c.
Observers in other frames will see that you get ever closer, but never reach c.

Where's my post gone ?

Your post was deleted because it is simply wrong. You can calculate what ever you want but that does not mean that you have actually calculated your correct speed. To get your actual speed you must measure it with respect to some point. It does not matter what point you choose to be stationary with respect to your motion you will never measure a speed greater then c.
 
  • #10
"you will never measure a speed greater then c." as seen from other frames. I was careful to say that.
You all seem to be missing the point.
If locked inside a ship experiencing acceleration you can only rely on acc. x time to calc your speed.
What distant observers see is irrelevant to you.
You will think you have exceeded c.

You have also deleted the interesting reference to the Wiki article on the Alcubierre method.
Be careful what you delete. I guarantee that I have been doing physics longer than anyone on this forrum. retired from Uni. a couple of years ago.
 
  • #11
map19 said:
You all seem to be missing the point.
If locked inside a ship experiencing acceleration you can only rely on acc. x time to calc your speed.

Right back at you. What is this acceleration measured with respect to, hm? The starting point? Well then assuming it is a constant acceleration is folly, as an observer at the starting point will not corroborate.
 
  • #12
map19 said:
"you will never measure a speed greater then c." as seen from other frames. I was careful to say that.
You all seem to be missing the point.
If locked inside a ship experiencing acceleration you can only rely on acc. x time to calc your speed.
What distant observers see is irrelevant to you.
You will think you have exceeded c.

You have also deleted the interesting reference to the Wiki article on the Alcubierre method.
Be careful what you delete. I guarantee that I have been doing physics longer than anyone on this forrum. retired from Uni. a couple of years ago.

We hear that a lot, 90% of the time it it pure BS. All we have to go one is post content.

Again, you can compute what ever you want, it does not make it your speed. If you attempted to use that computation for navagation you would be lost.
 
  • #13
daisey said:
If your question is "why can an object with mass physically not exceed the speed of light", I think you have already answered it. It would take an infinite amount of energy.
Wrong!

First of all an object does not have an intrinsic speed. An object can have a proper acceleration with any rate and any duration but it will always measure the speed of light to be c. It has absolutely nothing to do with a lack of energy.

At the same time, the speed between two objects (that have mass) [ remember this is relativity: there is no such thing as an intrinsic speed of an object ] is always less than c.

If you understand hyperbolic spaces you would realize that the limit of this speed does not exist, e.g. it is not c.
 
  • #14
Nabeshin said:
What is this acceleration measured with respect to, hm?
I do not know your level of comprehension but do you perhaps think that acceleration is relative?
 
  • #15
Passionflower said:
I do not know your level of comprehension but do you perhaps think that acceleration is relative?

You think it is not?

Will fellow passengers on the spaceship measure an acceleration between themselves and, say, the other passengers on the ship? Okay, well this is true of coordinate acceleration so we should explicitly state that we're talking about proper acceleration which is indeed invariant. Very good.

So our spaceship man feels some proper acceleration. However, if he wants to find a displacement he must obviously specify a reference point. In doing so, he chooses a second reference frame and can make the transformation from his proper acceleration to the coordinate acceleration his reference observer sees. Now he should be able to find out his speed with respect to this observer, and find it is in fact less than c.

MasterZoran or map19, do you take any issue with this? I believe that is all there is to say on the topic...
 
  • #16
Nabeshin said:
proper acceleration which is indeed invariant.
I am glad you know that.

Nabeshin said:
So our spaceship man feels some proper acceleration. However if he wants to find a displacement he must obviously specify a reference point.
You are not quite right on that one. While it is true that acceleration can change the observed distance and relative clock rates between two (point) objects with mass it does not cause a displacement as that would obviously violate the clock postulate. Displacement is caused by relative motion not by acceleration.
 
  • #17
Passionflower said:
I am glad you know that.


You are not quite right on that one. While it is true that acceleration can change the observed distance and relative clock rates between two (point) objects with mass it does not cause a displacement as that would obviously violate the clock postulate. Displacement is caused by relative motion not by acceleration.

What I mean is he wants to start writing down equations of motions, so he needs to start with displacement (x) in order to get velocity (v). Were I the guy on the spaceship, this is the way I would do it at least. Are you suggesting something differently, or just making caveats?
 
  • #18
Nabeshin said:
What I mean is he wants to start writing down equations of motions, so he needs to start with displacement (x) in order to get velocity (v). Were I the guy on the spaceship, this is the way I would do it at least.
But have you thought that through?

Suppose you go in such a spaceship and travel to a place 100 million light years away. Now what would be the practical information you want to know? ... Right, how long is it going to take me to get there. Then they tell you it will take 10 days.

So there you go, you covered 100 million light years in only 10 days, 10 million light years per day. Pretty fast wouldn't you say? So then what is your speed, well that all depends on how you define speed. :wink:

Now if you are in that ship would it really be of practical interest making calculations using some, what you called, reference point that is utterly irrelevant since time will evolve at least 200 million years for the quickest round trip? Right, I would not think so either! :biggrin:
 
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  • #19
Passionflower said:
So there you go, you covered 100 million light years in only 10 days, 10 million light years per day. Pretty fast wouldn't you say? So then what is your speed, well that all depends on how you define speed. :wink:

Velocity is distance divided by time*, where distance and time are both measured by the same observer.

In your example, the distance is measured in the "stationary" frame, but the time is measured in the "moving" frame. When we mix frames like that, we call it "celerity" or "proper velocity"**. There is no upper limit on celerity: the celerity of light is infinite.

_________________
*well, actually the derivative of displacement with respect to time, but I'll use simpler language here

**I don't like the term "proper velocity" because it's incompatible with other uses of "proper" in relativity, and it may mislead some people towards an incorrect definition of "proper acceleration".
 
  • #20
DrGreg said:
Velocity is distance divided by time*, where distance and time are both measured by the same observer.

In your example, the distance is measured in the "stationary" frame, but the time is measured in the "moving" frame. When we mix frames like that, we call it "celerity" or "proper velocity"**. There is no upper limit on celerity: the celerity of light is infinite.

_________________
*well, actually the derivative of displacement with respect to time, but I'll use simpler language here

**I don't like the term "proper velocity" because it's incompatible with other uses of "proper" in relativity, and it may mislead some people towards an incorrect definition of "proper acceleration".
Great post. In other words:

[tex]\phi=\frac{a\tau}{c}[/tex] is unbounded
but
[tex]v=c*tanh \phi[/tex] is always <c.
 
  • #21
starthaus said:
Great post. In other words:

[tex]\phi=\frac{a\tau}{c}[/tex] is unbounded
but
[tex]v=c*tanh \phi[/tex] is always <c.

Well, actually [itex]\phi=a\tau/c=\tanh^{-1}(v/c)[/itex], where a is constant proper acceleration (as measured by an object's accelerometer) and [itex]\tau[/itex] is proper time (as measured by the object's own clock) is neither velocity nor celerity, but a third way of measuring motion called "rapidity". Like celerity, it is unbounded and the rapidity of light is infinite.

This is in fact what map19 was talking about earlier, whether he/she realized it or not:
map19 said:
If locked inside a ship experiencing acceleration you can only rely on acc. x time to calc your speed.
What distant observers see is irrelevant to you.
You will think you have exceeded c.
 
  • #22
DrGreg said:
This is in fact what map19 was talking about earlier, whether he/she realized it or not:

You mean the wiki "proper" speed (celerity, as you call it) [itex]w=c*sinh\frac{a\tau}{c}[/itex].
 
  • #23
handwaving and saying 'infinite energy' is nonsense. As a physicist you know that infinite energy can't exist. no point mentioning it.
the conundrum is that could our ship communicate with it's take-off point it would be told that you are up to 99.99c, you are not increasing in speed, your length is almost zero, your mass is very high, and your time is very slow.
the ship would reply we still accelerate at 5g (say) we just measured the ship and it's still 100m long, since we are still accelerating at 5g the mass hasn't changed, and our clocks are ticking along nicely.
The changes seen from the remote take-off point have two different effects. If the ship now decellerates, arriving, say, at Hydra, normal length and mass are restored. Time, however, is different. Although only a few weeks might have elapsed on board, the Universe in general has aged 3 billion years.
Well, not exactly. Due to the Hubble factor Hydra is receding from us at about 6.1 x 10^7m/s. In 3 Bn years that figure will be about doubled. So if our ship orbits a planet at Hydra it has considerable relative recession velocity.
I would refer anybody with an interest to read the Davis and Lineweaver paper.

Oh yes, integral, I also worked on Apollo 13 to 16.
 
  • #24
map19 said:
handwaving and saying 'infinite energy' is nonsense. As a physicist you know that infinite energy can't exist. no point mentioning it.
the conundrum is that could our ship communicate with it's take-off point it would be told that you are up to 99.99c, you are not increasing in speed, your length is almost zero, your mass is very high, and your time is very slow.
the ship would reply we still accelerate at 5g (say) we just measured the ship and it's still 100m long, since we are still accelerating at 5g the mass hasn't changed, and our clocks are ticking along nicely.
The changes seen from the remote take-off point have two different effects. If the ship now decellerates, arriving, say, at Hydra, normal length and mass are restored. Time, however, is different. Although only a few weeks might have elapsed on board, the Universe in general has aged 3 billion years.

Aren't you mixing measurements from different frames again? To make physical sense, the measurements must be made by the same observer, as DrGreg stated above.
 
  • #25
map19 said:
handwaving and saying 'infinite energy' is nonsense. As a physicist you know that infinite energy can't exist. no point mentioning it.

I am not handwaving, you can read the proof in the first attachment of my blog. If you still don't understand why accelerating to c requires infinite energy after reading it, we can talk about it.
 
  • #26
Possible to cast a shadow that moves >c? The item that is blocking the light does not move at c or greater but the shadow cast further out could be greater?

I've heard that but never saw any proof.
 
  • #27
Not to derail the initial discussion, but I just want to let it be restated that the user Integral deleted another user's post in this discussion. That user wasn't going into original research and I've never seen anything like that on the physics forums before. The deletion of a well intentioned post is highly offensive to the spirit of this forum. I find this appalling.
 
  • #28
stevmg said:
Possible to cast a shadow that moves >c? The item that is blocking the light does not move at c or greater but the shadow cast further out could be greater?

I've heard that but never saw any proof.

You can show it with a rotating spotlight, like the one sent by one of the old lighthouses.
The sweeping speed of the spot is:

[tex]v=r \omega[/tex]

where

[tex]0<r<oo[/tex]

Keep [itex]\omega[/itex] fixed and make

[tex]r>\frac{c}{\omega}[/tex]

What value do you get for [itex]v[/itex]?

As an alternative, keep [itex]r[/itex] fixed and make:

[tex]\omega>\frac{c}{r}[/tex]

Bonus points: why doesn't the above violate the principles of special relativity?
 
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  • #29
starthaus said:
You can show it with a rotating spotlight, like the one sent by one of the old lighthouses.
The sweeping speed of the spot is:

[tex]v=r \omega[/tex]

where

[tex]0<r<oo[/tex]

Keep [itex]\omega[/itex] fixed and make

[tex]r>\frac{c}{\omega}[/tex]

What value do you get for [itex]v[/itex]?

As an alternative, keep [itex]r[/itex] fixed and make:

[tex]\omega>\frac{c}{r}[/tex]

Bonus points: why doesn't the above violate the principles of special relativity?

The "moving object" is not an object, not a photon and has no mass. Hence, it can move as fast as anything.
 

1. How fast is the speed of light?

The speed of light is approximately 299,792,458 meters per second, which is about 670 million miles per hour.

2. Why is the speed of light considered a limit?

The speed of light is considered a limit because no object with mass can travel faster than it. It is a fundamental law of physics known as the theory of relativity.

3. Can anything travel at the speed of light?

No, nothing with mass can travel at the speed of light. Only massless particles, such as photons, can travel at the speed of light.

4. What happens if something tries to go faster than the speed of light?

According to the theory of relativity, as an object approaches the speed of light, its mass increases infinitely and requires an infinite amount of energy to continue accelerating. This makes it impossible for anything to travel faster than the speed of light.

5. Why is the speed of light important to understand?

The speed of light is important to understand because it is a fundamental limit in the universe and plays a crucial role in many aspects of physics, including time, space, and energy. It also influences our understanding of the universe and how it behaves.

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