Is Speed an Illusion? Exploring the Physics of Speed

[megacal]

I don't understand why >= light speed is impossible.

If 2 objects are on a collision course and each is traveling >= 0.5 light speed,
aren't they essentially traveling at the speed of light relative to one another?

It seems that 0.5 light speed should be achievable...how much energy would it
require to propel e.g. 1,000 kg object to 0.5 light speed within 1 light year?

Or if it had X amount of continuous thrust for unlimited time, shouldn't it at some point
reach at least 0.5 light speed relative to it's starting point?

I'm not a physicist or mathematician...just trying to understand the concept of speed...it seems almost like an illusion...except when things collide and release energy.

 

[Nugatory]

I don't understand why >= light speed is impossible.

If 2 objects are on a collision course and each is traveling >= 0.5 light speed,
aren't they essentially traveling at the speed of light relative to one another?

Speeds don't add that way. The formula for adding speeds (google for "relativistic velocity addition") is
$$\frac{u+v}{1+\frac{uv}{c^2}}$$
not just u+v.

At low speeds the difference is insignificant, which is why we never notice this in ordinary life, but for speeds that are an appreciable fraction of the speed of light, it matters a lot.

 

[ghwellsjr]

I don't understand why >= light speed is impossible.

If 2 objects are on a collision course and each is traveling >= 0.5 light speed,
aren't they essentially traveling at the speed of light relative to one another?

It seems that 0.5 light speed should be achievable...how much energy would it
require to propel e.g. 1,000 kg object to 0.5 light speed within 1 light year?

Or if it had X amount of continuous thrust for unlimited time, shouldn't it at some point
reach at least 0.5 light speed relative to it's starting point?

I'm not a physicist or mathematician...just trying to understand the concept of speed...it seems almost like an illusion...except when things collide and release energy.

I covered this subject with many diagrams in this thread:

https://www.physicsforums.com/showthread.php?t=670436

Have a look and see if it helps.

 

[VantagePoint72]

Speeds don't add that way. The formula for adding speeds (google for "relativistic velocity addition") is
$$\frac{u+v}{1+\frac{uv}{c^2}}$$
not just u+v.

At low speeds the difference is insignificant, which is why we never notice this in ordinary life, but for speeds that are an appreciable fraction of the speed of light, it matters a lot.

While this is true, it may not be what OP had in mind.

If 2 objects are on a collision course and each is traveling >= 0.5 light speed,
aren't they essentially traveling at the speed of light relative to one another?

The velocity addition formula tells what the speed of one object will be in the other object's reference frame. Instead, OP may be asking, "In my reference frame, 2 objects are on a collision course and each is traveling >= 0.5 light speed. Aren't they traveling at the speed of light relative to one another in my reference frame?" The answer is yes (and emphasizes why specifying frames is essential in SR). In any particular reference frame, SR only restricts the velocity of objects in that frame. The maximum relative velocity between two objects in my frame is $2c$, not $c$.

 

[megacal]

Thanks for the earlier replies.
But the math, while clear to you, is Greek to me...actually more like ancient Krell.

"Aren't they traveling at the speed of light relative to one another in my reference frame?" The answer is yes

LastOneStanding,
do you mean you think that while it's not possible for an object to be thrust to >=1c, that
<2c is possible if each object is going >.5c towards another object also traveling >.5c
in the opposite direction?

In any particular reference frame, SR only restricts the velocity of objects in that frame. The maximum relative velocity between two objects in my frame is 2c, not c.

Wouldn't it have to <2c? BTW, I assume I'm "OP"(?) But "SR" =?


Thanks for trying to help me understand. I only have been exposed to under-grad calculus & physics. But would like to grasp the concepts in any case.

 

[VantagePoint72]

do you mean you think that while it's not possible for an object to be thrust to >=1c, that
<2c is possible if each object is going >.5c towards another object also traveling >.5c
in the opposite direction?

It's possible according to a third reference frame. The italics are critical. If object A is moving to my left at 0.6c and object B is moving to my right at 0.6c, then in my reference frame they are moving apart at 1.2c. However, it is not true that A is moving away from B faster than light in B's frame. To determine that, you have to use the formula you were given above, which gives about 0.88c in this case.

SR = "special relativity"

 

[megacal]

http://en.wikipedia.org/wiki/Velocity-addition_formula

Maybe at some point it will become clear, but for now
I"ll have to take your word for it and move on.

Thanks!

 

[nitsuj]

Thanks for the earlier replies.
But the math, while clear to you, is Greek to me...actually more like ancient Krell.



LastOneStanding,
do you mean you think that while it's not possible for an object to be thrust to >=1c, that
<2c is possible if each object is going >.5c towards another object also traveling >.5c
in the opposite direction?



Wouldn't it have to <2c? BTW, I assume I'm "OP"(?) But "SR" =?


Thanks for trying to help me understand. I only have been exposed to under-grad calculus & physics. But would like to grasp the concepts in any case.

That's one of the cool things about the topic of physics; it's about the concepts. Ultimately it's measurements of "observations", but "understanding" is the funner side anyways, (oh snap, sorry math fans)


Try taking a geometric perspective of c. From that I found it easier to "understand" how an physical thing wouldn't even "exist"* if it went passed c. There's no room for it in space OR time**. And those two dimensions in summation (read: continuum) is spacetime . So c is the limit to the geometry(read: spacetime) of this continuum.

Physics is ultimately about the measurements, but taking a geometric perspective of those measurements (easy enough with length, just bizarre with time for the uninitiated) makes it easier to "Understand" if, like me, you don't even know Newton physics, but are able to understand length, opps I see your an undergrad in physics.

*blackholes, and other gr "mysteries"
**among a host of other "reasons", like energy mass equivalence. Just different [STRIKE]measurements[/STRIKE] observations of/from the same phenomenon; c.

 

[megacal]

Try taking a geometric perspective of c. From that I found it easier to "understand" how an physical thing wouldn't even "exist" if it went passed c.

Thanks Nitsuj.

 

[PAllen]

"Is Speed an illusion?"

If only I could get the highway patrol to so believe ...

 

[megacal]

 

[ghwellsjr]

"Is Speed an illusion?"

If only I could get the highway patrol to so believe ...

Why? They might be giving out speeding tickets when you're parked.

 

[PAllen]

Why? They might be giving out speeding tickets when you're parked.

Nah, an illusion cannot meet evidentiary standards for conviction...