Thoughts?

Relativity states that as an object cannot surpass the speed of light because acceleration would cause its mass to become infinite. Objects already traveling faster than C are no in contradiction.
Acceleration is the derivative of velocity.
Velocity is the derivative of distance vs. time.

For some of you, derivative means the slope function.


The graph above is not differentiable. (It is a step)
I am interested in what others have to say. Discuss.

what is your question/thing to discuss?

The graph cannot have a 'near' vertical line because of the limit of speed of C. There is not a slope at the stepping point shown.
Theoretically, if velocity was a step graph, acceleration wouldn't exist even though an object changes position. No acceleration means no additional of mass.

The graph cannot have a 'near' vertical line because of the limit of speed of C. There is not a slope at the stepping point shown.
Theoretically, if velocity was a step graph, acceleration wouldn't exist even though an object changes position. No acceleration means no additional of mass.

ahh so basically you want to discuss how things can accelerate when theoretically arent?

Quote from: ﮎingulaЯiτy on November 04, 2008, 05:09:31 AM

The graph cannot have a 'near' vertical line because of the limit of speed of C. There is not a slope at the stepping point shown.
Theoretically, if velocity was a step graph, acceleration wouldn't exist even though an object changes position. No acceleration means no additional of mass.

ahh so basically you want to discuss how things can accelerate when theoretically arent?

Things accelerate.

ahh so basically you want to discuss how things can accelerate when theoretically arent?

According to the graph, an object changes position, but there is no acceleration, and therefore is no limit on speed. The only consequence is seen by the fact that speed is distance over time, and as the chart shows, the time is instantaneous for the transition of distance at the stepping point.

but remember, when your using a velocity graph of a real object, say like a car, its impossible for it to just jump to a higher speed, its always has an acceleration no matter how fast it is, so the graph is only a theoretical idea.
 

its impossible for it to just jump to a higher speed

The OP is only a thought experiment, but how do we know it is impossible to arrive at a destination without an in between area? Common experience and intuition would reject this notion, but it would also reject quantum mechanics.

so what you're saying is that its possible for something just to change its speed say from 10 to 20 mph with out accelerating. i cant really see that happen and also my question is how would that be possible.

Well objects can be in two places at the same time and move erratically in QM. An electron need not move in between two points. Hell, it can literally be in places at once. Extending these abilities to larger objects quickly reduces the possibility of it occurring naturally, and this thought experiment doesn't rule out future progress in advanced macro-field manipulations.

ok well im not an expert in QM, so im gonna try and stay away from that, but are you saying that its possible for say like a molecule or atom to be in two different places at the same time? i think i read something about that once. Im going to go look in the book and ill tell you if i find anything.

Yes, I am saying that. A rough example of why QM doesn't bleed through into the macro world, can be compared to flipping a coin. If you made a graph of the average of the flips, as the independent variable (number of flips) increases, the model gains stability approaching the middle or 1:1 mark.
After a few flips the model would appear erratic. After 100, it would not.

Quote from: Sexual Harassment Panda on November 04, 2008, 01:50:58 PM

its impossible for it to just jump to a higher speed

The OP is only a thought experiment, but how do we know it is impossible to arrive at a destination without an in between area? Common experience and intuition would reject this notion, but it would also reject quantum mechanics.

well the object didn't technically travel the distance, so it broke no laws of physics. In fact it didn't even move from its frame of reference. So since it didn't travel through the space in between these two points, this is perfectly valid.

From a relativistic standpoint a worldline has to be continuous to ensure that causality is obeyed (there can't be 'jumps' like in your picture), so if you were to join those two points with a spacelike (vertical) line you would be implying infinite acceleration, which is clearly impossible.

Quantum mechanically, the worldline would exist within a region of probabilities - if you knew for certain that at one instant the particle was at the empty circle, then you collapse it's wavefunction to that point in space-time.  This would mean that you have to allow the probability distribution to evolve again from that point, making the 'jump' you show impossible (it would the probability zero).

Does that help?

Any input to the discussion his help.
...There is not necessarily causality in QM though. Some extremely small particles already follow that outlined behavior.

Any input to the discussion his help.
...There is not necessarily causality in QM though. Some extremely small particles already follow that outlined behavior.

Which particles have been shown to violate causality? I've never heard of them 

Thoughts about life right? I have so many things in mind whenever we talk about life.

Thoughts about what?What specific thought ?Is it about life?

way to derail a good thread
let me rerail it
velocity.. QM particles what are you talking about QM jump

Spacelike (i.e. superluminal) QM jumps don't happen - as far as I know QM obeys causality

Superluminal implies speed, not redundant existence.

FTL travel is possible.  Einstein was wrong.

Reality is subjective, and science doesn't work.

FTL travel is possible.  Einstein was wrong.

He only said you can't accelerate past the speed of light. Which is still correct.

Quote from: WardoggKC130FE on November 08, 2008, 01:25:12 PM

FTL travel is possible.  Einstein was wrong.

He only said you can't accelerate past the speed of light. Which is still correct.

Yes, we can.

Quote from: WardoggKC130FE on November 08, 2008, 01:25:12 PM

FTL travel is possible.  Einstein was wrong.

He only said you can't accelerate past the speed of light. Which is still correct.

So what you mean is that we should be searching for a way to get to a higher velocity without accelerating to that velocity?

Quote from: Raist on November 08, 2008, 01:29:52 PM

Quote from: WardoggKC130FE on November 08, 2008, 01:25:12 PM

FTL travel is possible.  Einstein was wrong.

He only said you can't accelerate past the speed of light. Which is still correct.

So what you mean is that we should be searching for a way to get to a higher velocity without accelerating to that velocity?

Yes. There are particles traveling faster than the speed of light if I remember correctly.

edit: thought increasing velocity is acceleration. So.... yeah.

Quote from: Wendy on November 08, 2008, 01:32:03 PM

Quote from: Raist on November 08, 2008, 01:29:52 PM

Quote from: WardoggKC130FE on November 08, 2008, 01:25:12 PM

FTL travel is possible.  Einstein was wrong.

He only said you can't accelerate past the speed of light. Which is still correct.

So what you mean is that we should be searching for a way to get to a higher velocity without accelerating to that velocity?

Yes. There are particles traveling faster than the speed of light if I remember correctly.

edit: thought increasing velocity is acceleration. So.... yeah.

Right, but isn't acceleration a transient change in velocity? If you find a way to "jump", so to speak, to another velocity, you might be able to do it. And what are those particles? I haven't heard of them.

Quote from: Raist on November 08, 2008, 02:06:26 PM

Quote from: Wendy on November 08, 2008, 01:32:03 PM

Quote from: Raist on November 08, 2008, 01:29:52 PM

Quote from: WardoggKC130FE on November 08, 2008, 01:25:12 PM

FTL travel is possible.  Einstein was wrong.

He only said you can't accelerate past the speed of light. Which is still correct.

So what you mean is that we should be searching for a way to get to a higher velocity without accelerating to that velocity?

Yes. There are particles traveling faster than the speed of light if I remember correctly.

edit: thought increasing velocity is acceleration. So.... yeah.

Right, but isn't acceleration a transient change in velocity? If you find a way to "jump", so to speak, to another velocity, you might be able to do it. And what are those particles? I haven't heard of them.

No idea. I remember engy speaking of them.

edit: i found this http://en.wikipedia.org/wiki/Tachyon

Engy thinks the earth is flat, man.

Engy thinks the earth is flat, man.

No he doesn't.