# Time and limit velocity (speed of light)

## Main Question or Discussion Point

Hello. Today I've thinking about limit velocity and speed of ligth. We know that material particles can't achieve that speed, also when the speed of particles increases your own clock walks slowly. In the particular case of ligth your speed don't move anything.

This it a explanation of why particles can'r achieve the speed of ligth?:

I've in my mindt that maybe if the velocity of particles can increases higher than the speed of ligth this implies that the time of those particles must be negative, which is oposite to the arrow of time (for example in the second termodinamycs law way).

Has this any sense? Thanks. Sincerly.

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PeroK
Homework Helper
Gold Member
Hello. Today I've thinking about limit velocity and speed of ligth. We know that material particles can't achieve that speed, also when the speed of particles increases your own clock walks slowly. In the particular case of ligth your speed don't move anything.

This it a explanation of why particles can'r achieve the speed of ligth?:

I've in my mindt that maybe if the velocity of particles can increases higher than the speed of ligth this implies that the time of those particles must be negative, which is oposite to the arrow of time (for example in the second termodinamycs law way).

Has this any sense? Thanks. Sincerly.
Not really. The equations of SR (special relativity) are not well defined for a speed greater than $c$. You can't say anything about time for such hypothetical particles.

There are also causal problems if You hypothetically could send a message faster than light.

Ibix
We know that material particles can't achieve that speed,
More precisely, nothing with non-zero mass can travel at the speed of light.
also when the speed of particles increases your own clock walks slowly
It's not clear what you mean here. Clocks that are moving relative to you tick slowly as measured by you, yes. But the effect is symmetrical - your clocks tick slowly as measured by observers you say are in motion.
In the particular case of ligth your speed don't move anything.
It isn't possible to define time for things moving at the speed of light. And, again, the fact that something else is moving at the speed of light has no effect on your clocks.
This it a explanation of why particles can'r achieve the speed of ligth?:
It's a direct consequence of the postulates of relativity that you cannot accelerate past the speed of light. The speed of light is always the same in all inertial frames of reference. So no matter how fast you go, light always travels faster.
maybe if the velocity of particles can increases higher than the speed of ligth this implies that the time of those particles must be negative
This is not correct. Particles travelling faster than light (if any were possible) would be travelling backwards in time in some frames and forwards in others. This would make it possible to have causal paradoxes such as the "tachyonic anti-telephone". But this isn't why you can't exceed the speed of light. Rather, it's a consequence of the same postulates of relativity that make it impossible to exceed the speed of light.

PeroK
Homework Helper
Gold Member
This is not correct. Particles travelling faster than light (if any were possible) would be travelling backwards in time in some frames and forwards in others. This would make it possible to have causal paradoxes such as the "tachyonic anti-telephone". But this isn't why you can't exceed the speed of light. Rather, it's a consequence of the same postulates of relativity that make it impossible to exceed the speed of light.
Or, more prosaically, tachyons travel from A to B in one frame, and from B to A in another. Forwards in time in both cases.

Ibix
Or, more prosaically, tachyons travel from A to B in one frame, and from B to A in another. Forwards in time in both cases.
Or, perhaps better, it's not clear what "cause" and "effect" would mean if tachyons existed. At least, not without a re-write of relativity.

Ok, thanks I'm not enough knowledge for understand these questions at all. But I like to learn.

Yes, I know in relativity one must be very precise when one write, for example all people thinks that the clocks of another people go slowly. And also everybody is at rest with respect himself.

I know that relativity is based in the Michelson and Morley experiment and the limit velocity experiment, postulates of the theory can explain those experiments and predicts new ones.
But this is the question, It seems that the universe conspires so that nothing reaches the speed of light: why? Why is this speed so special?
then my reasoning (of little boy) was:
V<c --> delta time positive (arrow of time)
V=c --> delta time= zero
V>c --> delta time negative (opposite to arrow time)
We know that in our universe delta S is always positive and fixed the arrow of time.

Ok. not more speculations, this is not the place, I'm sorry. Can you suggest me some references for try to learn any more?

Mister T
Gold Member
But this is the question, It seems that the universe conspires so that nothing reaches the speed of light: why? Why is this speed so special?
If there's a speed that's the same for all observers regardless of their speeds relative to each other, then that speed has to be the fastest speed possible.

That's the only thing that makes that speed special.

Ok, thanks for your answers. The above link tells about I looking for. I showed you my "little boy reasoning" about the flow of time, velocity of objects and entropy. Then now I need to study. Articles in the above link can be a start point for that. If I had more questions I'll ask you. Thanks a lot.

I think you could also think of it like this: no matter what, there is a universal agreed upon speed that no one can reach; either this speed is infinite or it is finite. If it's finite, you will inevitably work out the math of special relativity. It turns out that experiment has repeatedly shown that the speed of light is the universal speed limit and that it is finite.

Furthermore, when you work out that math, you find that for an object to reach the speed of light, it requires (mathematically speaking) division by zero, and going faster than that will result in imaginary numbers for time, distance, momentum, etc. To me that's a good indicator that something reaching at or beyond light speed is nonsense.

For example, here is one of the most important mathematical expressions in special relativity: It is a function of velocity called the Lorentz factor:

$\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$

If v = c, you have

$\frac{1}{\sqrt{1 - \frac{c^2}{c^2}}}$
=
$\frac{1}{\sqrt{1 - 1}}$
=
$\frac{1}{\sqrt{0}}$
=
$\frac{1}{0}$

which is obviously nonsense.

If v > c, say, 2c, you have

$\frac{1}{\sqrt{1 - \frac{(2c)^2}{c^2}}}$
=
$\frac{1}{\sqrt{1 - 4\frac{c^2}{c^2}}}$
=
$\frac{1}{\sqrt{1 - 4}}$
=
$\frac{1}{\sqrt{-3}}$

and now you have the square root of negative 3.

If this were applied to relativistic momentum, you'd have a momentum of

$p = \frac{mv}{\sqrt{-3}}$
=
$p = \frac{mv}{i\sqrt{3}}$
=
$p = \frac{-imv}{\sqrt{3}}$

so you have a negative imaginary momentum. (note: to go from i-1 to -i, first change i-1 to 1/i, then multiply the numerator and the denominator by the conjugate, which since there is no real part is just i/i.)

Basically if you move as fast or faster than the speed of light you end up with nonsense. That's probably not the best way to look at it, but if you have made it past algebra, it's a great crutch.

Yes, I know these equations and concepts, for example in the first above article, that I've been reading: http://arxiv.org/abs/physics/0302045v1, the way of deduction the addition speed law is in the same way I make the deduction of Lorentz transforms (except for some little bit nuances). Notice that eq.7 and eq.8 don't have the same symmetry and it's essential.

Also is very interesting the final discussions about the values of K. One needs to make K in a range of values that corresponds with the experiments such Michelson Morley and limit speed. Then, the only consistent values for K are positive values. This arguments gives us the well know equations of SR.

But why is necessary that this happened in this way. Well, I think that Physics study the Universe only in the way of the human people can perceive that Universe. And we needs to order the events and then we needs the time, also how it was said above we need to preserve the cause-effect relationship. And limit speed takes account of that.

But really at higher energies velocity don't make big grows, is the mass that grows. And we say that mass is given by Higgs bosom. Will may the Higgs boson (interaction with the Higgs field) increase the mass of a particle to infinity as special relativity requires?

Ok with the above articles I've enough for begin to learn a little bit about that, I don't like speculations, I know that physics are experiments and equations. Then I don't like to continue spell like in the above paragraph. Thanks everybody for your help.

jbriggs444
Homework Helper
2019 Award
But really at higher energies velocity don't make big grows, is the mass that grows.
The sort of mass that grows is "relativistic mass". The concept of relativistic mass is not used much. Instead, we normally use the concept of "invariant mass" which does not grow.

One thing that does grow with higher velocity is momentum. The momentum of an object with non-zero invariant mass increases without bound as the speed of light is approached.

The sort of mass that grows is "relativistic mass". The concept of relativistic mass is not used much. Instead, we normally use the concept of "invariant mass" which does not grow.

One thing that does grow with higher velocity is momentum. The momentum of an object with non-zero invariant mass increases without bound as the speed of light is approached.
Thanks. That's means that at higher energies the Higgs field don't needs to work more hard? I like to get god concepts. : -)

Yes, I know these equations and concepts, for example in the first above article, that I've been reading: http://arxiv.org/abs/physics/0302045v1, the way of deduction the addition speed law is in the same way I make the deduction of Lorentz transforms (except for some little bit nuances). Notice that eq.7 and eq.8 don't have the same symmetry and it's essential.

Also is very interesting the final discussions about the values of K. One needs to make K in a range of values that corresponds with the experiments such Michelson Morley and limit speed. Then, the only consistent values for K are positive values. This arguments gives us the well know equations of SR.

But why is necessary that this happened in this way. Well, I think that Physics study the Universe only in the way of the human people can perceive that Universe. And we needs to order the events and then we needs the time, also how it was said above we need to preserve the cause-effect relationship. And limit speed takes account of that.

But really at higher energies velocity don't make big grows, is the mass that grows. And we say that mass is given by Higgs bosom. Will may the Higgs boson (interaction with the Higgs field) increase the mass of a particle to infinity as special relativity requires?

Ok with the above articles I've enough for begin to learn a little bit about that, I don't like speculations, I know that physics are experiments and equations. Then I don't like to continue spell like in the above paragraph. Thanks everybody for your help.
You’re putting too much emphasis on mass. Just let m be mass and look at the momentum equation.

As for the asymmetry between eq 7 and eq 8, it’s based on experithece: space and time are not exactly symmetical. Space is isotropic, as mentioned just before those equations. But is time? Perhaps with “micro” physics, but clearly cracked eggs do not uncrack themselves. In a closed system, entropy either increases or remains constant. We can’t turn around in time like we can in space. Any derivation of transformation equations that represent our universe will have to take that into account.

As for k being less than zero, that brings up inconsistencies according to your paper, and in the recent discussion where we discussed a similar derivation, k<0 brings indeterminate forms. So it makes no real sense.

You’re putting too much emphasis on mass. Just let m be mass and look at the momentum equation.
Yes, that's true, perhaps because my capital book in SR was the A.P. French book. I think is a very good book, but it does a very big emphasis in the relativistic mas.

Of course mass is an invariant, how could I be so stupid!! I'm not a professional in relativity and only can study in my free time... and relativity is very complex and if for some time I can't work in it I forgets concepts and ideas.

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Yes, that's true, perhaps because my capital book in SR was the A.P. French book. I think is a very good book, but it does a very big emphasis in the relativistic mas.

Of course mass is an invariant, how could I be so stupid!! I'm not a professional in relativity and only can study in my free time... and relativity is very complex and if for some time I can't work in it I forgets concepts and ideas.
It’s really just a name. “Relativistic mass” was chosen before physicists really had time to interpret the theory in a simpler, more concise way. Minkowski helped with that, and people realized notions like relativistic mass just overcomplicated things.

Nugatory
Mentor
And we say that mass is given by Higgs boson. Will may the Higgs boson (interaction with the Higgs field) increase the mass of a particle to infinity as special relativity requires?
That's means that at higher energies the Higgs field don't needs to work more hard?
It's not true that "mass is given by the Higgs boson". There is a connection between mass and the Higgs field, but it's not what you'd think it is from what's being written in the popular press. One B-level explanation that is not hopelessly wrong (but bears about the same relationship to the real explanation as a child's book does to a college-level textbook) is https://futurism.com/one-huge-misconception-about-the-higgs-boson-video/

But for purposes of understanding relativity, it's safe to just completely ignore all the Higgs stuff - it's pretty much totally unrelated.