Exceed The Speed Of Light?
Suppose you and your friend are traveling in space, each in your own wonder car that allows you to travel at c , the speed of light.
True or false: If you and your friend each drive at the speed of light but in opposite directions, then he will be moving at twice the speed of light relative to you.
Use Einstein's theory of relativity
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2 solutions
This question and it's placement in the Classical Mechanics section is a little misleading. The only hint to use special relativity in determining the answer is in the reference to the speed of light. However, the spacecraft and the individuals in the equation are large objects, they are not elementary particles. Large objects behave in manners predicted by Classical Mechanics, therefore it is reasonable to assume the answer is True.
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Sorry, But there was no other section for Relativity, So i had to post it in classical mechanics.
where does this equation come from ? this doesn't make sense to me!! If this is true , let me add a stationary object too to the system .
So you are telling that the stationary object and the the car have have same relative velocity with respect to the other car??
okkay this is like proving 1=0 using the properties of tan90
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Good Pointing out! This is why matter can't travel at speed of light. If it would then 1 = 0 is true.
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Stephen Hawking once said that if the object is made to travel in space infinitely and indefinitely at one point of time it can achieve the speed of light and will be forever...
I made minor research on the topic and accordingly i could find this is true!! but this is assumed to be an arbitrary situation only , and making a car go at the speed of light almost requires half of the energy of whole universe !!
According the theory of lorentzian relativity a object carves the fabric of space and time in order that at any reference space the velocity of light is the same !!
The correct answer would be true and your equation would not be used for what the question asked.
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If it is true then wouldn't it defy special theory of relativity.
So, what will be used sir?
Yea I don't know physics but .... I am aware of Einstein so given the T F nature of the question... I went against intuition lol
Well,the problem is nice. But unfortunately, it defies Special Theory of Relativity.Thus, it does not have any realistic significance.
would the equation still be true if the frame of reference, with respect to which the individual speed is measured, itself moves with the speed of light in the direction of one of the car?
is this the general equation for relative velocity? that, for cases related to motion of bodies very low to the speed of light, the denominator is taken as 1 and that is why we write rel. velocity= v2-v1?
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No, It is not general. It is just for two parallel moving objects.
For more info Read This
Where did you get this equation from? Velocity of B with respect to A = v(B) - v(A)
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Actually your formula is derived from the formula above for small velocities.
For more info Read This
To be honest, you can just use ur common sense to figure this out without using the equation you provided. Btw, nice question!
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how?unless relativity is "common sense" to you, by that i mean knowledge you obtain from everyday experiences.The equation he provided is actually against usual human experiences,if we kick a ball with speed v on a truck of speed a we will think that the ball's speed would be v + a which is wrong
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The issue with understanding problems involving light is that our everyday experiences don't prepare us for the information we glean when studying relativity. To boil down the special theory of relativity in a very basic level, we see that the speed of light (in a vacuum) will be measured by any observer to be c (3*10^8 m/sec). This measurement is independent of the direction of travel of the light or the observer. In the given problem, the two objects were moving at c in opposite directions, but since the speed of light is always measured to be c, either object will measure the other's velocity as c, not 2c.
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@Tim Gallacher – It would be 2c.... because u are moving in the opposite direction either towards or away.... so wht if the speed of light is measurred as c.... both the observers will feel that they are moving towards or away at a sped of 2c......only when one is stationary the speed observed is c of the light... but practically it is impossible even to see the object with naked eye...
the balls speed will be v+a......... as the initial velocity of the ball will be ..v so the ball will appear traveling at a speed of a to the observer on the truck... t
I totally agree with the equation, in fact, that is the right method of solving this problem. I agree with your justification as well. However, what I meant was, you can also predict the answer using your imagination and common sense. Sorry for the misunderstanding, what you stated above is absolutely correct. Cheers!
yup thats what i did
Can someone explain this in English please? I don't get it
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whole construct of time will change for them .so when they measure the speed it would still be c due to the change in time factor . even their biological clock would be in sync with the cahnge in time so they wont feel that
this is english
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@Hamza A – c = the speed of light. Substitute the speed of light for each velocity into the relative velocity equation (where each object is moving away from each other at rate c), and you will get the relative speed of c.
Depends on the observer. If a stationary person views both cars then yes they will be moving at twice the speed of light away from each other. You cannot deny after one year, each will be 2 light years apart from one and other. However, relative to eachother is a whole other issue. Firstly, if you're travelling at the speed of light, time will freeze. But obviously you will not know this because you will also be frozen. So you yourself will have been travelling a vast distance without a single second going past, that's a second of time relative to you. Or to put it another way,you will experience the sensation of teleportation. This was all a brain exercise an I have no references. I look forward to being proven wrong :)
just because the cars will be 2 light years apart doesn't mean that both of them traveled at 2 c. It's not wright. of you now presume that they did travel at 2 c then they should be 4 light years apart. so it's just wrong. The law in simple terms is this: speed of light is constant in any reference sistem. Time contracts relative to another observer but not for the person in the car. I mean the observer would see the time contraction. To solve the problem the easiest way just keep in mind that speed of light is constant in any reference sistem and the answer will be FALSE. For a mathematic and rigorous explanation see Sachim's comment
It is true that I will find my friend moving with twice the speed of light relative to me......that is the concept of relative velocity... one thing is sure that u wont be able to see ur friend as speed of light just cannot be felt by naked eye... but the answer just cannot be false.... as there is no definite proof for the answer to be false... or may be cannot be determined can be the next best option....but, not false...
taking the ideal case...(assuming we can see objects moving at the speed of light)...we should be seeing our friend move with double the speed of ours...since it's not actually light that's moving...it's a car moving with that speed...unlike light it has a momentum and mass...it can be seen; unlike light consisting of photons or maybe waves...
When we say infinity(i) what is 2i ? The thing is not 2i doesn't exist but in our patterns 2i is as absurd as i itself. 2i surely will start existing once we get the knowledge of i. Hence for equations based on our existing patterns may hold good for C here but actually it will be 2C
He will not be viewing at all. ;-) BTW nice explanation.
Actually we have relative velocity for two parallel moving objects as : V rel = 1 − c 2 V A V B ∣ V B − V A ∣ .
So, we have V rel = 1 − c 2 c ( − c ) c − ( − c ) = 2 2 c = c .