Adding two velocities

mayflow

I saw on this forum a formula by Einstein in his special relativity theory something like

Velocity sum = (velocity one plus velocity two)/ (1+velocity1*velocity2/the speed of light squared)

With small velocities, they simply seem to add together, but at higher velocities, they add less and less together. So, does this imply that high velocities warp space? I guess that is what it says, hmmm? But how? Does increased velocity expand space?

I put the formula into an excel spreadsheet and played a bit and I also notice that if velocities can exceed the speed of light, if you add them, they get slower, at least up until they are each 1 quintillion meters per second, in which case they equal to zero, and no matter how much larger the velocity from there, they still add to zero.

What does this imply?

bcrowell

v1 and v2 both have to be less than c.

mayflow

I= more than c, now what? Quantum entanglement?

Pengwuino

You gave people 4 hours in a saturday morning. What do you expect?

What do you mean " I = more than c"? You can't have velocities greater than the speed of light. If you do, then you have the nasty issue of what does it mean to have an imaginary velocity (and a whole chain reaction of non-sense begins if you want to assume that makes sense).

DaveC426913

Seeing as to get to a velocity near c in the first place, you will have to start with some lower velocity (which will be less than c), then when you add another velocity to it (which will also necessarily be lower than c) using the formula, you will never be able to reach a number that's higher than c.

So: no slower than light v can ever reach or exceed c.


HOWEVER...


You have a point that it doesn't really forbid higher than c numbers, but they must start > c - and using the velocity formula you should see that they will never go below c.

You have stumbled upon the case for the hypothetical particles known as tachyons.

mayflow

Well, it is arguable that any velocity is imaginary, and I just don't see any reason why the speed of light needs to be enforced upon innocent drivers if they want to go faster. ((Just saying that I don't believe light (which is just an electromagnetic wave in the frequency spectrum visible to our eyes) is non supersedable in speed.) There just seems to be something missing here.

It is still anti-intuitive to me that two light beams approaching each other are not adding speeds. If you drive down the road one way and I approach from the other way and we are each going 60MPH, we approach each other at 120 MPH. In the special relativity velocity formula, if we changed the speed limit to 60 MPH, we would be approaching each other at 60 rather than 120 MPH. Safer, yes. Realistic, no.

mayflow

Light or any electromagnetic wave doesn't function like me starting to run or a vehicle
getting up to speed. You turn a light on or you broadcast an RF wave and it instantly is at top speed. This is likely why Einstein used it as a constant. In that regard, I can see why he did so. WOW, isn't that interesting? In a sense light is binary - either on or off.

I am glad I found this forum. You guys really get me thinking.

Gigasoft

As an exercise, write down the Lorentz transformation that corresponds to a velocity v in the x direction, and apply it to the description of a particle moving at velocity w in the same direction. Find the relationship between the resulting x' and t' coordinates. What do you get?

mayflow

I haven't any education in higher maths, but I can understand simple algebra - would you mind explaining to me the math in that link? Please take it slow and simple (elegant) for me.

jtbell

No we don't. I "see" you approaching with a speed that is a whisker less than 120 MPH, and you "see" me approaching with the same speed. You can work out the exact number with the velocity-addition formula.

mayflow

I can but what proves this formula to be correct? Remember my first post? If you implement a speed of 1 quintillion meters per second and another of equal or greater velocity, there would be zero speed. Does the equation actually have any real truth to it?

DaleSwanson

Yes, see the sticky in this forum that links to this page:
What is the experimental basis of Special Relativity?

mayflow

I don't care about that. I am talking about a certain formula, and whether it is correct at speeds beyond the speed of electromagnetic waves or not. If it does hold true beyond the speed of electromagnetic waves, it means that more increasing velocity eventually stops time dead cold in its tracks.

JaredJames

Just so I'm on the right track, the problem you're outlining is that the equations don't work with imaginary (impossible) speeds?

MikeLizzi

The velocity addition formula is derived by taking the derivative of the transformation equations. The Lorentz factor, Gamma, does appear in some of the initial setup equations but eventually drops out in the case of adding (or subtracting) velocities in the same direction. As you know Gamma is undefined for velocities >= c so an equation that contains Gamma cannot apply for any velocity >= c. Additionally all equations that are derived from that equation have the same limitation even if Gamma is no longer present. The physics textbooks seem to assume everybody knows that. Bad assumption.

I know of another example in Newtonian Physics where the same kind of misunderstanding can take place. (I was a victim of that misunderstanding.)

P.S. Most of the big guns on this forum appear to be taking a break. They deserve it.

jfy4

It doesn't really matter how you "feel" or what you "believe" in this circumstance. I've said it before, some really thorough thinkers here have said it before, and I'll say it again, If you think that velocities should just add, then nature disagrees, and that's the bottom line. Special relativity has been tested not only numerous times, but in a multitude of different ways, and all tests indicate that in the energy limits appropriate, special relativity is accurate.

Its good to have some intuition, but don't let it keep you from getting to know nature better, nature has spoken.

Pengwuino

No. Unless you can tell me what it means to have [tex]3i[/tex] apples in my hand, then it does not make sense for me to talk about having an imaginary velocity.

Intuition falls apart as you approach light speed. Your idea that velocities add in the newtonian sense is accurate to within the precision that you can typically measure it. If you actually went out and drove two cars at each other at 60 MPH, you'd see them close at something like 120.0000000001mph due to the relativistic effects. Now, can you detect something that is ~0.0000000001% of a difference between Newtonian and relativistic velocity additions? No.

Now when you start colliding particles at large fractions of the speed of light, the differences become extremely obvious.