Defies Logic?

[Shark Bait (Stu)]

I have been listening to reports and reading articles about recent events at CERN's LHC.

Quote: At full power, trillions of protons will race around the LHC accelerator ring 11 245 times a second, travelling at 99.9999991% the speed of light. Two beams of protons will each travel at a maximum energy of 7 TeV (tera-electronvolt), corresponding to head-to-head collisions of 14 TeV. Altogether some 600 million collisions will take place every second.

So......

If two cars have a head on collision and they are both travelling at 100km/h, the combined speed of the impact is going to be 200km/h.

If two protons collide, travelling at 99.9999991% the speed of light they will NOT have a combined impact velocity that is faster than the speed of light. I have trouble visualising this as it seems to defy logic.

Science states that any object (or sub-atomic particle) cannot reach the speed of light as they have mass.

Any thoughts that can help make this clear would be greatly appreciated.

Thanks.
Stu.

[Larryp (Laurie)]

The 2 cars do not have an impact speed of 200kph. They both come to a stop from 100kph. This is an often misunderstood concept.

[Shark Bait (Stu)]

Originally Posted by Larryp

The 2 cars do not have an impact speed of 200kph. They both come to a stop from 100kph. This is an often misunderstood concept.

Embarrassed.... looks like I am going to be hitting up the local library for some Physics textbooks. Thanks for the feedback Laurie.

[Astro_Bot]

I can recommend General Relativity by I.R. Kenyon. More readable than many, but not so light weight that it skips over important bits. There is some maths, though, but then that's kinda essential to show how relativity works.

[Shark Bait (Stu)]

Thanks for the book suggestion RG. I will look into it. I enjoy trying to understand the articles that I read surrounding this topic but to be honest, I tend to end up more confused than before I started.

[Astro_Bot]

Glad I could help, but keep in mind that book is a text, not a light Sunday read.

[LAW (Murphy)]

Don't forget that E^2=m^2.C^4 + p^2.C^2 (Which is just saying that E only = mc^2 in it's 'rest' state or 'non-relativistic' state.

The energy of the collision increases because of inertia, when protons are travelling at the speeds they are capable of reaching in the LHC their mass increases by (correct me if I'm wrong) a factor of 7000.

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[sjastro]

Originally Posted by Shark Bait

I have been listening to reports and reading articles about recent events at CERN's LHC.

Quote: At full power, trillions of protons will race around the LHC accelerator ring 11 245 times a second, travelling at 99.9999991% the speed of light. Two beams of protons will each travel at a maximum energy of 7 TeV (tera-electronvolt), corresponding to head-to-head collisions of 14 TeV. Altogether some 600 million collisions will take place every second.

So......

If two cars have a head on collision and they are both travelling at 100km/h, the combined speed of the impact is going to be 200km/h.

If two protons collide, travelling at 99.9999991% the speed of light they will NOT have a combined impact velocity that is faster than the speed of light. I have trouble visualising this as it seems to defy logic.

Science states that any object (or sub-atomic particle) cannot reach the speed of light as they have mass.

Any thoughts that can help make this clear would be greatly appreciated.

Thanks.
Stu.

This is where mathematics helps in resolving this apparent defying of logic.
The approach velocity of two cars travelling at 100 km/hr is in fact 200 km/hr.

The approach velocity is derived in special relativity by the equation
(u+v)/(1+uv/c^2) where u and v are the velocities of the objects moving towards each other.

For the two cars in the example 100 km/hr = 0.0000055c
In the equation the uv/c^2 term for the cars is (0.0000055cx0.0000055c)/c^2 = 1.008X10^-16 which is a very small number.

The approach velocity of objects travelling at speeds well below c is
(u+v)/(1+uv/c^2) = u+v as the uv/c^2 term is very small.

Hence the approach velocity of the two cars is 100 + 100 = 200 km/hr.

Suppose there are two objects travelling towards each other at 0.9c
Now the uv/c^2 term is no longer small and equals (0.9cx0.9c)/c^2 =0.81.

The approach velocity is (0.9c+0.9c)/1.81 = 0.995c.
The approach velocity can never exceed c.

For two photons approaching each other at c, uv/c^2 = 1, and the approach velocity is (c+c)/2 = c.

Regards

Steven

[Dave2042 (Dave)]

Stu

If I could draw a distinction which is extremely important in modern physics.

This certainly defies 'common sense' or ordinary day-to-day intuition. However it doesn't defy logic, as all the maths and physics 'fits together' properly, and what we observe matches what the theory says we should.

The issue is that our ordinary intuitions are based on the fact that we only see (and have evolved to deal with) a tiny bit of the universe, being where things are medium-sized and move slowly. Outside that, when you think about it, there's really no reason for us to have reliable intuitions about things.

[Shark Bait (Stu)]

Originally Posted by LAW

Don't forget that E^2=m^2.C^4 + p^2.C^2 (Which is just saying that E only = mc^2 in it's 'rest' state or 'non-relativistic' state.

The energy of the collision increases because of inertia, when protons are travelling at the speeds they are capable of reaching in the LHC their mass increases by (correct me if I'm wrong) a factor of 7000.

Thanks Murphy.

Good video. Every little bit of information helps put the pieces of the puzzle in their place.

Originally Posted by sjastro

This is where mathematics helps in resolving this apparent defying of logic.
The approach velocity of two cars travelling at 100 km/hr is in fact 200 km/hr.

The approach velocity is derived in special relativity by the equation
(u+v)/(1+uv/c^2) where u and v are the velocities of the objects moving towards each other.

For the two cars in the example 100 km/hr = 0.0000055c
In the equation the uv/c^2 term for the cars is (0.0000055cx0.0000055c)/c^2 = 1.008X10^-16 which is a very small number.

The approach velocity of objects travelling at speeds well below c is
(u+v)/(1+uv/c^2) = u+v as the uv/c^2 term is very small.

Hence the approach velocity of the two cars is 100 + 100 = 200 km/hr.

Suppose there are two objects travelling towards each other at 0.9c
Now the uv/c^2 term is no longer small and equals (0.9cx0.9c)/c^2 =0.81.

The approach velocity is (0.9c+0.9c)/1.81 = 0.995c.
The approach velocity can never exceed c.

For two photons approaching each other at c, uv/c^2 = 1, and the approach velocity is (c+c)/2 = c.

Regards

Steven

Cheers Steven.

Thank you for taking the time to go through the explanation in detail. I now understand why people see 'beauty' in equations.

Originally Posted by Dave2042

Stu

If I could draw a distinction which is extremely important in modern physics.

This certainly defies 'common sense' or ordinary day-to-day intuition. However it doesn't defy logic, as all the maths and physics 'fits together' properly, and what we observe matches what the theory says we should.

The issue is that our ordinary intuitions are based on the fact that we only see (and have evolved to deal with) a tiny bit of the universe, being where things are medium-sized and move slowly. Outside that, when you think about it, there's really no reason for us to have reliable intuitions about things.

Apologies Dave.

I was stuck for a title. I agree that these questions go beyond what the majority can fully comprehend (me included). That is probably what makes it so interesting.

[Dave2042 (Dave)]

Apologies Dave.

I was stuck for a title. I agree that these questions go beyond what the majority can fully comprehend (me included). That is probably what makes it so interesting.[/QUOTE]

Apology entirely unnecessary, I think your post was interesting and reasonable.