Special relativity - What if the speed of light was infinite?

[pinkerpikachu]

Special relativity -- What if the speed of light was infinite?

Suppose the speed of light was infinite. What would happen to the relativistic predictions of length contraction and time dilation?

Okay, so I know all of this is based on the concept of the constancy of the speed of light. So would the whole theory just go kurplunk?

and

Explain how the length contraction and time dilation formulas might be used to indicate that c is the limiting speed in the universe.

?? help on that one too pleasee

 

[DaveC426913]

This is homework. You need to show your attempts at an answer.

 

[diazona]

Suppose the speed of light was infinite. What would happen to the relativistic predictions of length contraction and time dilation?

Okay, so I know all of this is based on the concept of the constancy of the speed of light. So would the whole theory just go kurplunk?

Not "constancy" really, but "invariance" - that is, the speed of light is the same in different reference frames.

But anyway, think about what happens to the formulas of relativity as the speed of light gets larger and larger.

 

[pinkerpikachu]

Sorry, I wouldn't just ask for an answer like that if had any idea of how to solve it. Special relativity just blows my mind and I was hoping to clear up a few things in my brain with the answer to these questions. But here goes nothing:

Okay. So, length contraction, the equation is: L(root(1-v^2/c^2)). If C --> infinitity i guess i'd be like taking a limit (maybe? except I don't know how)
the number from the root would be infinitely small (right?) because a number over an infinitely big number is a very small fraction which is made even smaller by the root. Could I then say that that number is basically zero? And then zero * L is zero. Therefore L' is zero.

but I don't understand what that tells me...wikipedia tells me that the answer is the length observed by an observer in relative motion with respect to the object.

not quite sure what that means? I don't really understand what length contraction is.

But I understand what time dilation is a little bit better.

Time dilation = that time is measured according to the relative velocity of the reference frame it is measured in, time is measured to pass more slowly in any moving reference frame as compared to your own

um...but what would this mean if the speed of light was infinite? I guess...well, we've figured that if the speed of light remains constant then time cannot. But if it was infinite would that mean it was everywhere at once? I think we'd lose the whole reference frame thing that from the postulates of special relativity. So how would we compare anything to anything else?

Then next question: this one I'm really not sure about. Taking a guess:

well it is theory that anything with mass cannot travel the speed of light. And everything around us has mass? or something like that, so therefore it is impossible for anything to travel the speed of light.

right?

I'm not sure how I would go about proving this with the length contraction and time dilation formulas though.

 

[Cyosis]

Taking the limit c->\infty is the right idea. However the root will not vanish. What is \lim_{c \to \infty}=v^2/c^2?

 

[DaveC426913]

um...but what would this mean if the speed of light was infinite? I guess...well, we've figured that if the speed of light remains constant then time cannot. But if it was infinite would that mean it was everywhere at once? I think we'd lose the whole reference frame thing that from the postulates of special relativity. So how would we compare anything to anything else?

As Cyosis points out, rather than looking at infinity, look at what would happen if c were simply larger than it is, then what would happen if c were so large it approached infinity.

Then next question: this one I'm really not sure about. Taking a guess:

well it is theory that anything with mass cannot travel the speed of light. And everything around us has mass?

(Well, energy doesn't, but let's get back to the question.)

You may be overthinking it.
What happens to length and time as a massive object approaches c? What would happen to length and time if an object could somehow reach or exceed c? Do you get sensical answers?

 

[pinkerpikachu]

Taking the limit c->\infty is the right idea. However the root will not vanish. What is \lim_{c \to \infty}=v^2/c^2?

I have very limited knowledge of taking limits. Um...is it undefined or zero?
I took some notes in class, and for length contraction I have the formula and then: as v --> c, L --> 0
oh wait! I forgot there was a one in the formula. So if v^2/ c^2 is just a really small number, then 1 minus that number is basically just 1. and the square root of one is 1.

So then, Lo times 1 is just Lo. So nothing would expand or contract?

and then the same thing for time. It'd just be to (time not). So would this mean that nothing was changing?

You may be overthinking it.
What happens to length and time as a massive object approaches c? What would happen to length and time if an object could somehow reach or exceed c? Do you get sensical answers?

Well, as I said earlier, as v -> c (for length contraction), L --> 0? Right? But I'm having trouble fully understanding what that means.

for time dilation, what I wrote down was: as v --> c then t --> infinity.

I understand the time dilation. Infinity is just not an answer that makes sense. But what does the L = 0 tell me?

 

[fluidistic]

I'm probably not helping the OP, but considering the speed of light as infinite isn't it what we do in classical physics? (Newtonian physics). So that there's no length contraction, there exists simultaneity, etc?

 

[Cyosis]

So if v^2/ c^2 is just a really small number, then 1 minus that number is basically just 1. and the square root of one is 1.

So then, Lo times 1 is just Lo. So nothing would expand or contract?

and then the same thing for time. It'd just be to (time not). So would this mean that nothing was changing?

This is correct.

I'm probably not helping the OP, but considering the speed of light as infinite isn't what we do in classical physics? (Newtonian physics). So that there's no length contraction, there exists simultaneity, etc?

There is no speed limit in classical mechanics, while there is a speed limit of c in relativistic mechanics. Therefore you would expect that if you let c go to infinity, or in other words if you do not have a speed limit, the Lorentz transformation goes to the Galilean transformation. In other words classical mechanics can be obtained from special relativity by removing the speed limit. This is what you would expect.