A Physics Quiz of a different type

[DonRotolo]

Last night, the neighbors came over for a visit, and (somehow) we got on the topic of Relativity. One neighbor, a non-science kind of guy (but very intelligent) wanted to know why you can't go faster than the speed of light.

My response was that at one end of E=MC^2 you have pure mass, and at the other end you have pure energy. You can't go past the endpoints. As you go closer to C, M decreases and E increases, since C is decreasing*

*That is, since C is relative to a fixed point, as you hit, say, 0.75 C, there is only 0.25 C "left", so C is actually smaller.

OK, he accepted that as reasonable , but in my mind, that's not right.

So, in one or two sentences, why is there a limit to the speed of light?

Thanks.

[msimon785]

From Wikipedia:

Upper limit on speeds
According to special relativity, the energy of an object with rest mass m and speed v is given by γmc2, where γ is the Lorentz factor defined above. When v is zero, γ is equal to one, giving rise to the famous E = mc2 formula for mass-energy equivalence. Since the γ factor approaches infinity as v approaches c, it would take an infinite amount of energy to accelerate an object with mass to the speed of light. The speed of light is the upper limit for the speeds of objects with positive rest mass.[31]

More generally, it is normally impossible for information or energy to travel faster than c. One argument for this follows from the counter-intuitive implication of special relativity known as the relativity of simultaneity. If the spatial distance between two events A and B is greater than the time interval between them multiplied by c then there are frames of reference in which A precedes B, others in which B precedes A, and others in which they are simultaneous. As a result, if something were travelling faster than c relative to an inertial frame of reference, it would be travelling backwards in time relative to another frame, and causality would be violated.[Note 4][33] In such a frame of reference, an "effect" could be observed before its "cause". Such a violation of causality has never been recorded,[15] and would lead to paradoxes such as the tachyonic antitelephone.[34]

[the man]

This is only a theory. Some scientist believe that you can go faster than the speed of light, we just have no idea how to do it. A particle accelerator in Europe actually detected what they believe to be partials that can travel faster than the speed of light. I personal think it will be possible to go faster than the speed of light in the future.

[RoboMaster]

Originally Posted by the man

A particle accelerator in Europe actually detected what they believe to be partials that can travel faster than the speed of light.

Are you talking about the neutrinos a month or so back? There was a lot of healthy speculation about that. I heard that was finally shown to be false, they got the timing between the start and endpoints wrong. They had used GPS for the timing and their error was something like they had forgot to completely take general relativity into account for calculating the time (the relative time was different because the satellites were moving fast)
Someone please correct me if I'm wrong or show a link or reference if I'm right. I can't find where I heard that.

I find the Wikipedia explanation pretty good. It should be noted what the gamma factor is (the funny y). The Wikipedia article refers to how it approaches infinity, etc., so it may be helpful to see what it actually is. It often (or almost always) pops up in the math for these types of equations, so they made a variable for it.



Oh, here's a joke. The tachyon is a hypothetical particle that would move faster than light. So...
The barkeeper says, "Hey, we don't serve tachyons here," and a tachyon walks into the bar.

[Tristan Lall]

Originally Posted by the man

This is only a theory. Some scientist believe that you can go faster than the speed of light, we just have no idea how to do it. A particle accelerator in Europe actually detected what they believe to be partials that can travel faster than the speed of light. I personal think it will be possible to go faster than the speed of light in the future.

It's fine to believe something, if you have a good reason for it. Here you just need to be a little more careful adding up the facts. Even the experimenters who published those results are skeptical, and are calling for independent replication of the results. (Wikipedia has a fantastic article on those results and their implications.) I wouldn't bet on the original results being upheld.

That's not to say we haven't been wrong about our understanding of the universe before—only that our understanding of the universe today is several orders of magnitude greater than in any other era of history, and because of this, experimental error is the more likely explanation for the results you mention.

Besides, any application of faster-than-light anything is still firmly within the realm of speculation (or daydreaming)—in other words, I don't think there's any good reason to believe "it will be possible to go faster than the speed of light in the future".

Also, "only a theory" doesn't really mean what you imply. Wikipedia has a dense article on theories, but the important concept is that "theories are collections of hypotheses that are logically linked together into a coherent explanation of some aspect of reality and which have individually or jointly received some empirical support". In other words, calling something a theory doesn't call it into question so much as it indicates that there has been systematic scientific inquiry into the subject.

Aside: 4 citations to Wikipedia in 4 replies? That must be a record. (And it's not a bad thing.)

I'm no expert mathematician, but I believe Don said he wanted an answer in "one or two sentences", and nobody has provided anything less than a paragraph related to the subject.

Being a high school student that has not taken physics yet, this question is very interesting, and I would also appreciate a short and concise answer, instead of having to read 4 long paragraphs.

In conclusion, I would very much be interested in a short answer as to WHY it isn't possible to go faster than the speed of light.

Thanks!

"In order for knowledge to be understandable, it must be accessible. We live in a world today where people don't want to read long books to learn things. Bring the knowledge to the people, and they will learn it". - Sal Khan, Khan Academy

[RoboMaster]

Yeah, you're right on the simplification part.
The Wikipedia article mentioned this, I'll try to sum it up.

It takes an increasing amount of energy to approach the speed of light, in a way that you would need an "infinite" amount of energy to travel at the speed of light.
The physics of relativistic motion, which deal with speeds comparable to the speed of light, show that the mass (or relativistic mass) increases as you approach the speed of light and the energy of the object approaches infinity. So, it takes more energy to move something more massive, and infinitely so when approaching the speed of light.

Cool!

[Ether]

Particle "A" is traveling at c/2 in the +X direction in inertial reference frame XY. Particle "B" is traveling at speed c/2 in the -X direction in the same reference frame. See Figure 1.

In a second inertial reference frame X'Y', particle "B" is at rest. How fast is particle "A" traveling in this second reference frame? See Figure 2.

[DonRotolo]

Originally Posted by RoboMaster

It takes an increasing amount of energy to approach the speed of light, in a way that you would need an "infinite" amount of energy to travel at the speed of light.

OK, so because E=ymC^2 (y being gamma), and because gamma approaches infinity as v approaches C, we end up where you need an infinite amount of energy to accelerate just past C.

As for Al's' thing with the flashlights, an observer standing still would see a solid beam of light, just hanging there in the air, like an infinite, glowing sausage.*



*Not really, but it's cool to think about that, no?

[Ether]

Originally Posted by DonRotolo

you need an infinite amount of energy to accelerate just past C.

Just equal to c, for any object with non-zero rest mass.

[DonRotolo]

Originally Posted by Ether

Just equal to c, for any object with non-zero rest mass.

Well, wouldn't you be able to reach c, but not exceed it?
That means you CAN reach c. Going past c is what requires infinite energy, reaching c needs just a smidgen less than infinity.

And yes, we're assuming the object rest mass is nonzero

[Aren Siekmeier]

Originally Posted by DonRotolo

Well, wouldn't you be able to reach c, but not exceed it?
That means you CAN reach c. Going past c is what requires infinite energy, reaching c needs just a smidgen less than infinity.

And yes, we're assuming the object rest mass is nonzero

As v -> c, y -> inf, so we cannot even get to c because the "infinite energy" is when you reach c.

At v=c, B=v/c=1, so y=1/sqrt(1-B^2) is already undefined (or infinity, if that's how you want to define dividing by zero).

[Ether]

Notes embedded in red below

Originally Posted by DonRotolo

Well, wouldn't you be able to reach c, but not exceed it? That means you CAN reach c.

No, you wouldn't be able to reach c.

Going past c is what requires infinite energy, reaching c needs just a smidgen less than infinity.

Reaching c requires infinite energy.

And yes, we're assuming the object rest mass is nonzero

I see Aren beat me to it.

[the man]

Its an asymptote.