# Objects colliding at c

Hello, I was wondering how collisions would when both objects are travelling at c.

Imagine 2 cars driving towards each other at a constant speed on a perpendicular course at regular speeds (not at c). Depending on how high their speeds are and their initial starting positions are they could miss each other or crash into each other in a variety of ways, ignoring the chance that they miss or that hit exactly on the right spot, there would be a certain chance for car A to hit car B's side, and the other way around.

Whenever one of the cars (car B) travels at c instead, car A would always see B approaching at c no matter how fast it go itself. Because of this B could still easily crash into A's side, but as long as A isn't at c itself, then the chances would be almost impossible for A to crash into B's side. While B is moving at c, it seems it makes absolutely no difference what A's speed is to determine the chances of which cars side will be hit because A would always see B approaching at c.
So if speed doesn't matter, what happens if they are both at c? Would they always miss, or hit each other on the sweet spot on the corner? Or do they just have a 50% chance to hit each other on the sides.

Of course mass can't travel at c, so feel free to substitute cars for a line of photons moving towards another line of photons.

## Answers and Replies

I'm trying to figure out the difficulty of this question.

Imagine I'm in a car driving at speed c.
My friend is driving in the other car at speed c.

If we started driving at exactly the same time, and are displaced from the center at exactly the same distance, we will hit each other.
If my friend started driving a bit sooner than I did, we may possibly not hit each other.. depending on how much I waited before starting to drive, and how long our cars are...
I do not see the difference between driving at speed c vs some other speed in this case..

Integral
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Since massive objects cannot reach c your question has no answer.

I'm trying to figure out the difficulty of this question.

Imagine I'm in a car driving at speed c.
My friend is driving in the other car at speed c.

If we started driving at exactly the same time, and are displaced from the center at exactly the same distance, we will hit each other.
If my friend started driving a bit sooner than I did, we may possibly not hit each other.. depending on how much I waited before starting to drive, and how long our cars are...
I do not see the difference between driving at speed c vs some other speed in this case..

Well first of all, time dillation and length contraction kick in. Would a car be infinitely compressed making it impossible to hit anything? Wouldn't time dillate in such a way that both cars wouldn't notice anything of their path and would rather arrive instantaneously at their destination? How could it collide with something if it arrives instantaneously from its perspective?

Also, when its said that they see each other arriving at c, what exactly does this mean? Doesn't it mean seeing it move at a speed of c relative to its own movement? That seems to be what is measured at least. If the two cars would be behind each other and would be moving alongside the same path, then I couldn't imagine them ever colliding, but wouldn't the front car still see the car behind it approaching at c? Or does this frame of reference thing only apply when one of them is moving at a speed less than c? What does seeing something approach at c even mean when time dilation makes everything seem instant?

It may be very simple, but I'm getting quite confused about these frames of references and such.

Since massive objects cannot reach c your question has no answer.

No answer.. Well what about two lines of photons which are extremely long and contain an infinite amount of photons within them that are on a crash course? Would photons of line A ever have the same position as photons on line B? If so, which photons if the photons of the lines would be equally far from the collision point.

Drakkith
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Science Advisor
How could it collide with something if it arrives instantaneously from its perspective?

They would not arrive instantly at their destination, they would travel at whatever speed they were going and arrive in a finite amount of time.

What does seeing something approach at c even mean when time dilation makes everything seem instant?

Objects with mass, such as cars, CANNOT travel at c. Ever.

It may be very simple, but I'm getting quite confused about these frames of references and such.

Time dilation would affect both cars if they are moving, as would length contraction. Since each car would be moving perpendicular to each other both would view length contraction of the other car. If the cars were heading towards or away from each other length contraction would not be observed.

Xilor said:
Well first of all, time dillation and length contraction kick in.

http://en.wikipedia.org/wiki/Ladder_paradox
http://en.wikipedia.org/wiki/Relativity_of_simultaneity

Xilor said:
If the two cars would be behind each other and would be moving alongside the same path, then I couldn't imagine them ever colliding, but wouldn't the front car still see the car behind it approaching at c?

Let's say I'm going at speed c, and my friend is at speed c. My friend is a meter behind me, and we are going in the same direction. While I am traveling at the speed of light, time inside of my car is frozen. I see what my friend is right in back of me, and that is all I will be seeing until I stop going at the speed of light. I cannot measure speed of anything around me as time does not change for me while I'm in the car.

I hope you understand this..

Drakkith
Staff Emeritus
Science Advisor
Let's say I'm going at speed c, and my friend is at speed c. My friend is a meter behind me, and we are going in the same direction. While I am traveling at the speed of light, time inside of my car is frozen. I see what my friend is right in back of me, and that is all I will be seeing until I stop going at the speed of light. I cannot measure speed of anything around me as time does not change for me while I'm in the car.

Again, objects with mass cannot travel at c.
Even assuming you could do it you wouldn't even be capable of "seeing" anything, as like you said time would not pass for you.

ghwellsjr
Science Advisor
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If the cars were heading towards or away from each other length contraction would not be observed.
You must mean something other than what you said here. Can you please explain?

Drakkith
Staff Emeritus
Science Advisor
You must mean something other than what you said here. Can you please explain?

To my knowledge length contraction is only observed when an object is moving perpendicular to the observer, not towards or away from. Or rather that is only the perpendicular motion of the object compared to the observer that will determine the length contraction.

DaveC426913
Gold Member
To my knowledge length contraction is only observed when an object is moving perpendicular to the observer, not towards or away from. Or rather that is only the perpendicular motion of the object compared to the observer that will determine the length contraction.

No. Two trains passing each other (or one train passing through a station) will be measured as compressed along the train's axis of motion.

DaveC426913
Gold Member
Well what about two lines of photons which are extremely long and contain an infinite amount of photons within them that are on a crash course? Would photons of line A ever have the same position as photons on line B? If so, which photons if the photons of the lines would be equally far from the collision point.

Photons do not have a valid frame of reference, so it too is a meaningless question.

What you need to understand is this:

Two cars rushing toward each other cannot attain the speed of light, they can get arbitrarily close to it.
If both cars are traveling toward each other at near c with respect to a stationary observer between them, they do not observe each other as approaching faster than c. Relativistic velocity addition uses the Lorentz Transform, and will always result in a total closing speed of less than c.

For example, two cars travelling at .99c wrt to a third observer do not see the other as approaching at 1.98c. Applying the Lorentz Transform you get a closing speed of more like .9999c.

If they were instead both travelling at .9999c wrt a middle observer, they would measure each other closing at something like .9999999c.

It's too late tonight for me to do the actual numbers - these are just spitballing.

http://en.wikipedia.org/wiki/Lorentz_transformation

Photons do not have a valid frame of reference, so it too is a meaningless question.

If a photon does not have a frame of reference at all, how does a photon interact with anything? Shouldn't photons just move past everything then if they could never 'see' themselves at the same position as another particle? If they could 'see' that, why is it a meaningless question then?

Dale
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If a photon does not have a frame of reference at all, how does a photon interact with anything?
Why would having a frame of reference have anything to do with being able to interact? What law of physics requires that?

I don't know, I don't know why these questions are branded as meaningless either so I'm trying to figure out why.
If photons could interact with photons, would the two lines of photons questions suddenly become relevant then?

DaveC426913
Gold Member
I don't know, I don't know why these questions are branded as meaningless either so I'm trying to figure out why.
If photons could interact with photons, would the two lines of photons questions suddenly become relevant then?

The thing is that you are arbitrarily swapping massive objects and massless objects into the same thought experiment. They are very different.

Massless objects (such as photons) always travel at c, and do not have a reference frame.
Massive objects (such as atoms) can never travel at c, and do have a reference frame.

One of the ways of defining a frame of reference is as 'that frame in which the observer is at rest'. So, for a photon to have a frame of reference means it must be at rest in this FoR. But photons, as massless particles, are defined as always travelling at c in all reference frames. How can there exist a reference frame in which the photons is simultaneously at rest and moving at c?

Dale
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I don't know, I don't know why these questions are branded as meaningless either so I'm trying to figure out why.
If photons could interact with photons, would the two lines of photons questions suddenly become relevant then?
Photons can interact with photons. You can google "two photon physics".

Regarding why the question is meaningless, we have a FAQ entry on the topic that we are in the process of revising, but here it is in its current form.
https://www.physicsforums.com/showthread.php?t=511170

The bottom line is that the questions are meaningless because they contain a premise which is specifically forbidden by the very theory which you are seeking to use to answer the question. If you were to ask what Euclidean geometry says about the interior angles of a triangle with sides of length 10, 5, and 3 it would also be a meaningless question for a similar reason, the premise is specifically forbidden by the theory.

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Well if a photon being at a certain position is a meaningless statement, then how do these interactions take place exactly? I'm not asking for a photon to be at rest at a position, but there has to be some sort of positional information somewhere right? Even if its just a chance to be at a certain position.

Dale
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2021 Award
Well if a photon being at a certain position is a meaningless statement, then how do these interactions take place exactly? I'm not asking for a photon to be at rest at a position, but there has to be some sort of positional information somewhere right? Even if its just a chance to be at a certain position.
Sure, it is meaningful to talk about a photon's position in an inertial frame, particularly if you are neglecting quantum effects (I.e. Using "photon" as short hand for "a very brief highly collimated classical pulse of light").

What is meaningless is the idea of a photon's frame or perspective. And a massive object traveling at c is forbidden by SR. As long as you avoid both of those pitfalls you will be able to ask reasonable questions and get reasonable answers.

Drakkith
Staff Emeritus
Science Advisor
No. Two trains passing each other (or one train passing through a station) will be measured as compressed along the train's axis of motion.

Hmm, so an object traveling at 0.99c will appear length contracted no matter what direction it is traveling relative to me? (I'm stationary in this frame) If it's coming at a 45 degree angle towards me it will look length contracted exactly like it would if its motion is at a 90 degree angle (perpendicular) to me?

ghwellsjr
Science Advisor
Gold Member
As long as both you and the object are inertial (neither of you are accelerating, either by changing your speeds or your directions) then you can consider the object to be length contracted along its direction of motion.

But what does it mean that it is coming toward you at some angle? It is either coming directly toward you or will miss you by some distance. In either case, it's angle relative to you will vary by about 180 degrees. It could appear to you in very strange ways as it passes toward you, then past you, but any way that you measure its length will remain constant. And it will measure your length contracted by the same amount.

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Drakkith
Staff Emeritus
Science Advisor
As long as both you and the object are inertial (neither of you are accelerating, either by changing your speeds or your directions) then you can consider the object to be length contracted along its direction of motion.

But what does it mean that it is coming toward you at some angle? It is either coming directly toward you or will miss you by some distance. In either case, it's angle relative to you will vary by about 180 degrees. It could appear to you in very strange ways as it passes toward you, then past you, but any way that you measure its length will remain constant. And it will measure your length contracted by the same amount.

Got it!