Why can't we reach to Speed of light at Space?

[pvk21]

According E=mc2,the law that shows nothing
may travel faster than the speed of light. Because of the equivalence of energy and mass, the energy which an
object has due to its motion will add to its mass. In other words, it will make it harder to increase its speed. This
effect is only really significant for objects moving at speeds close to the speed of light. For example, at 10
percent of the speed of light an object's mass is only 0.5 percent more than normal, while at 90 percent of the
speed of light it would be more than twice its normal mass. As an object approaches the speed of light, its mass
rises ever more quickly, so it takes more and more energy to speed it up further. It can in fact never reach the
speed of light, because by then its mass would have become infinite, and by the equivalence of mass and
energy, it would have taken an infinite amount of energy to get it there. For this reason, any normal object is
forever confined by relativity to move at speeds slower than the speed of light. Only light, or other waves that
have no intrinsic mass, can move at the speed of light.
This what Stephen hawkings explained in his book. (brief history of time)

 

[phinds]

According E=mc2,the law that shows nothing
may travel faster than the speed of light.

No. Massive objects cannot travel at c, but E=m^2 has nothing to do with it.

 

[uumlau]

I'm pretty sure that's incorrect. I wouldn't include the uncertainty of position into the calculation of the velocity like you've done. At minimum I'd bet that it's not as simple as measuring the position of the particle just twice and determining the velocity from those two measurements. And positrons are absolutely not electrons traveling backwards in time.

However I admit I'm not an expert in quantum physics, so i could be mistaken.

No. You're applying HUP to a classical Newtonian particle (as if it were moving at .999c and a little jump would bring it to 1.0001c).
In fact, applying HUP to a relativistic Einsteinian particle, a particle moving at .999c would get a little jump to .9999c, as per the Lorentz transform.

Thanks for your replies. I'm not using the Heisenberg Uncertainty Principle, though it seems I am. Note that I said, "Very roughly speaking," in order to present a more simplified view of what was going on for those who aren't as familiar with quantum mechanics. More formally speaking, when figuring out probability amplitudes for a particle going from one state to another and back, you get the result that, "there is an amplitude for particles apparently to propagate faster than the speed of light."

Source: R. P. Feynman in his 1986 Dirac Memorial Lecture on "The Reason for Antiparticles". Key quote at t = 1:50


This does not mean that the particles "go faster than the speed of light" in any sort of macro-measurable way. Just that the math indicates, quite surprisingly, that you have to account for seemingly impossible path integrals that include superluminal velocities. It is this result that implies antimatter must exist, at least as virtual particles.

 

[DaveC426913]

Huh. did not know that.

It is this result that implies antimatter must exist, at least as virtual particles.

But you don't mean antimatter, you mean tachyons.

Antimatter certainly exists (anti-protons, anti-electrons, anti-neutrons) , and has nothing to do with superluminal velocities.

 

[Drakkith]

Thanks for your replies. I'm not using the Heisenberg Uncertainty Principle, though it seems I am. Note that I said, "Very roughly speaking," in order to present a more simplified view of what was going on for those who aren't as familiar with quantum mechanics. More formally speaking, when figuring out probability amplitudes for a particle going from one state to another and back, you get the result that, "there is an amplitude for particles apparently to propagate faster than the speed of light."

Okay. Like you said, it's very fuzzy when it comes to quantum effects. Just so I'm not confused, the particle is not being accelerated past the speed of light, right? It's not really even traveling faster than c. It simply has some probability to be found at a position that is further away than a classical object could get to in time no matter its velocity. Is that a semi-accurate understanding?

 

[uumlau]

Okay. Like you said, it's very fuzzy when it comes to quantum effects. Just so I'm not confused, the particle is not being accelerated past the speed of light, right? It's not really even traveling faster than c. It simply has some probability to be found at a position that is further away than a classical object could get to in time no matter its velocity. Is that a semi-accurate understanding?

Yeah, it's more of a mathematical artifact than a physical phenomenon you could measure in a particle accelerator, for example. What we know for sure is that if our math needs to include this possibility of antiparticles in order to be accurate, and we do measure that accuracy that proves the math to be correct. In the case that Feynman is talking about in the video (his visual aids are mostly invisible, sadly, due to poor quality), the start and end points of the particle are entirely within the light cone. It's the theoretical perturbations of that path (necessary for the Feynman path integrals - which is its own topic) that go outside the light cone.

Quantum mechanics is full of stuff like this, where the math says thus-and-such, but it's easy to misinterpret it such that it "violates" causality. Quantum entanglement, especially, leads people to making wild assertions of faster than light travel or reverse causality, just because they forget that a "wave function collapse" is a mathematical thing that describes changes to the system, not a real thing. Look up the "quantum eraser" to read/watch several such (bogus) arguments. The physics is real, but the conclusions drawn about violating causality are bogus interpretations.

Even classical physics has the occasional mathematical construct that travels faster than light (without carrying information). The phase velocity of light is one such that can exceed the speed of light: http://en.wikipedia.org/wiki/Phase_velocity

 

[uumlau]

Okay. Like you said, it's very fuzzy when it comes to quantum effects. Just so I'm not confused, the particle is not being accelerated past the speed of light, right? It's not really even traveling faster than c. It simply has some probability to be found at a position that is further away than a classical object could get to in time no matter its velocity. Is that a semi-accurate understanding?

Yes. My original statement was inaccurate to the degree that it implied the particle would exceed the speed of light in a directly measurable way. That's the problem with trying to simplify the explanation of something that is really rather complex, and why I included my preemptive "Very roughly speaking" disclaimer.

In the example Feynman is using, the start and end points of the particle are entirely within the light cone. It's the mathematics of the perturbation (necessary for Feynman path integrals - which is its own topic) that requires analyzing perturbations outside the light cone. We would never measure the particle itself exceeding the speed of light in any meaningful way, but we can measure that the results of the perturbation math are extremely accurate and thus the math is forced to include these superluminal perturbations.

Quantum mechanics is full of oddities like this that lead to assertions of faster-than-light travel or even reverse causality. The concepts of "wave function collapse" and "entanglement" are especially responsible for such bogus interpretations. Look up the "quantum eraser" experiments to see how these interpretations go. Don't get me wrong, the physics is real, but the interpretations that somehow something traveled backwards in time to cause the results are bogus.

Even classical physics has mathematical artifacts that appear to travel faster than the speed of light, e.g., the phase velocity of light in a dispersion medium: http://en.wikipedia.org/wiki/Phase_velocity

 

[guywithdoubts]

Watching some videos recently the—what I assume is the proper name—spacetime diagram showed up; in case I'm mistaking it for something else, I'm talking about the very plain diagram with time as one of the axis and space as the other.
In this diagram, as you accelerate and move further in space, you also "move less" in time, since the curve becomes almost plain. Is this not a good way to look at it? That if you kept accelerating more and more, all you'd achieve is getting too close to no movement in time, which for a body with mass is nonsense?

 

[DaveC426913]

That if you kept accelerating more and more, all you'd achieve is getting too close to no movement in time, which for a body with mass is nonsense?

Far from nonsense, that is perfectly accurate.
It'll get asymptotically close, but never reach it.

 

[Neandethal00]

The problem is that as the speed of an object increases so does the mass at normal speeds this is pretty insignificant but as yuo approach the speed of light the mass of the object approaches infinity.

Mass and velocity are two totally unrelated physical parameters.
They shouldn't even be remotely related, but special relativity somehow made mass dependent on velocity.
Is it something wrong in our very definition of mass and speed?

 

[Drakkith]

Mass and velocity are two totally unrelated physical parameters.
They shouldn't even be remotely related, but special relativity somehow made mass dependent on velocity.
Is it something wrong in our very definition of mass and speed?

No, why would there be?

 

[phinds]

Mass and velocity are two totally unrelated physical parameters.
They shouldn't even be remotely related, but special relativity somehow made mass dependent on velocity.
Is it something wrong in our very definition of mass and speed?

No, you have simply bought into a pop-science misconception called "relativistic mass" which has been deprecated for decades.

Think about it this way: if mass were actually dependent on speed, then an object would have to have an infinite number of different values for its mass, all at the same time, because it has an infinite number of different speeds, depending on the infinite number of reference frames that one can choose to look at it from. Clearly doesn't work.

 

[uumlau]

Mass and velocity are two totally unrelated physical parameters.
They shouldn't even be remotely related, but special relativity somehow made mass dependent on velocity.
Is it something wrong in our very definition of mass and speed?

No, the "mass" isn't dependent on velocity. The "mass-energy" is dependent on velocity.

The easiest way to look at it is with the equation E^2 = p^2 + m^2 ($c$ is set to "1" here, for mathematical convenience.)

The $m$ in the equation above is the actual mass of whatever object you are dealing with. $p$ is its momentum, and $E$ is its energy.

If the object is sitting still, then $$E = m,$$ or, adding the $c$ back in, $$E = mc^2.$$ (This should be a very familiar equation to you! )

Photons, however, have no mass. Photons and all massless objects instead have $$E = p,$$ or $$E = pc$$

If you have a system of objects and/or particles, the total effective mass of the system (how hard is it to push, how much it bends space-time to generate gravity) is a sum of all the masses, $m$, plus the contributions from the momentum of each. This includes all of the electrons and protons and neutrons and such, along with any photons or other massless particles that are part of the system. This is a simplistic, cartoonish version of the actual physics, of course. The real version involves stress energy tensors and general relativity.

However, since it's kind of silly to bring in full-fledged general relativity in for just determining how forces will interact with a single particle, you can use the short cut of saying that the "effective mass" of the particle is $m\gamma$, because the momentum of the particle is $m\gamma v$, where $\gamma$ is the the Lorentz factor from special relativity.

Read here for more detail, including the minor controversy on whether "relativistic mass" is a useful concept: http://en.wikipedia.org/wiki/Mass_in_special_relativity

The main problem with the concept of relativistic mass is that it leads to misunderstandings such as exemplified by your post. No, the "mass of the object itself" is not changing, but it seems to be implied that it is. It's just a convenient way of doing calculations in very simple systems.

 

[AgentSmith]

So, let's say I, in my close to c spaceship, pass three observers. One is traveling close to my speed in my direction with a difference of 100 mph. I pass another standing on a planet in a relatively...there's that word again...stationary position. And a third in a spaceship going the other direction at near c.

Now, as I understand it two things are happening.

As to actual relative speeds...

I pass the first with an actual difference in speed of about 100 mph. I actually pass the observer on the planet at near c. As to the third, I actually pass him at near 2c, actual theoretical velocity.

Now to the second thing.

The first observer observes me pass him at about 100 mph since relativistic effects are minimal at those speed differences. The second has considerable relativistic observational warpages but thinks I'm going near c. The third doesn't observe the actual near 2c velocity difference. To both me and the other guy, we both will never observe the other going greater than c. To each of us the most we can hope to observe is each other traveling away from each other at no more than c.

Is that close to correct?

tex

Sorta kinda. You have to use the Lorenzt equations to find your velocity from different observers view. You can find tutorials on this at World Science University. You will never observe anyone traveling at c, not just faster than c.

 

[Soul Intent]

I will not pretend that I am an expert, but I do know that the laws of physics break down at that speed correct?

Only if the object has a predetermined mass.

 

[phinds]

Only if the object has a predetermined mass.

No the laws don't break down for massive objects at that speed, they show that you can never GET to that speed, as has already been pointed out.

 

[Soul Intent]

No the laws don't break down for massive objects at that speed, they show that you can never GET to that speed, as has already been pointed out.

Yeah but something like a photon could get to that speed. The only reason a massive object can't accelerate to the speed of light is being it has mass.

 

[phinds]

Yeah but something like a photon could get to that speed. The only reason a massive object can't accelerate to the speed of light is being it has mass.

Yes. Your point being?

And by the way, it is not "a photon could get to that speed", it's "a photon has to travel at that speed and only that speed (in a vacuum)"

 

[Drakkith]

There is a subtle but important difference between a photon getting to c and being at c. A photon doesn't accelerate up to c. From the moment it is created to the moment it is absorbed it travels at c.

 

[PWiz]

After reading many (confused?) posts in this thread, I'm finally beginning to appreciate the decision of discarding "relativistic mass" from common scientific literature nowadays. It tends to make people think that the fact that an object has any mass at all is a result of choosing a particular coordinate system.

 

[Monsterboy]

I think you are right , what the OP asked is that , if any object( spacecraft in this case) is accelerated continuously in space without running out of fuel , why can't that object reach or exceed the speed of light ?

I found this when I googled http://physics.about.com/od/relativisticmechanics/f/SpeedofLight.htm
So, according to this link , you can travel at the speed of light but you will need infinite amount of energy to do so.

The universe itself has finite amount of energy (first law of thermodynamics) hence you can't travel at the speed of light.
I hope someone with a background in this subject validates the information in this link.

That would better be interpreted as "because there is no such thing as an infinite amount of energy, objects with mass cannot travel at the speed of light".

Agent Smith, this is a misleading argument. It implies that the reason we cannot reach the speed of light is a limitation of the propulsion. This is not so.

Even a "magical" propulsion system that had unlimited thrust, unlimited fuel and unlimited time will never reach c.

In fact, it is the laws of the universe itself that prevent us from reaching the speed of light. The nature of the limit is time dilation.

So the article i provided is wrong ?

 

[DaveC426913]

So the article i provided is wrong ?

From post #33?

Er... Any specific part?

 

[rootone]

So the article i provided is wrong ?

If you mean the article posted just above, the article is right, but you have misunderstood it.
Since an infinite amount of energy is something which cannot physically exist then it's impossible for an object with mass to travel at the speed of light..
Don't be thinking 'Well an objectt could travel at light speed if it had that energy available' - That amount of energy is not available, infinity i not a normal number.
Infinite energy is impossible, so therefore travel at light speed is impossible.

 

[Monsterboy]

From post #33?

Er... Any specific part?

Yes ... http://physics.about.com/od/relativisticmechanics/f/SpeedofLight.htm

Slower Than the Speed of Light
The next major set of particles (so far as we know, all of the ones that aren't bosons) move slower than the speed of light. Relativity tells us that it is physically impossible to ever accelerate these particles fast enough to reach the speed of light.

Why is this? It actually amounts to some basic mathematical concepts

Since these objects contain mass, relativity tells us that the equation on the top right of this page determines the kinetic energy of the object, based upon its velocity. Notice the denominator which contains the variablev (for velocity). As the velocity gets closer and closer to the speed of light (c), that v2/C2term will get closer and closer to 1 ... which means that the value of the denominator ("the square root of 1 - v2/C2") will get closer and closer to 0.

As the denominator gets smaller, the energy itself gets larger and larger, approaching infinity. Therefore, when you try to accelerate a particle nearly to the speed of light, it takes more and more energy to do it. Actually accelerating to the speed of light itself would take an infinite amount of energy, which is impossible.

 

[phinds]

Yes, this says exactly what WE have been saying. If you think otherwise then you are somehow misinterpreting it.

 

[DaveC426913]

I was going to say that the idea of 'not being able to approach c because of mass increase' is an outdated explanation.

 

[Monsterboy]

Even a "magical" propulsion system that had unlimited thrust, unlimited fuel and unlimited time will never reach c.

As the denominator gets smaller, the energy itself gets larger and larger, approaching infinity. Therefore, when you try to accelerate a particle nearly to the speed of light, it takes more and more energy to do it. Actually accelerating to the speed of light itself would take an infinite amount of energy, which is impossible.

Yes, this says exactly what WE have been saying. If you think otherwise then you are somehow misinterpreting it.

I just equated "unlimited fuel" and "infinite amount of energy" ,then Dave's statement goes like this " Even a "magical" propulsion system that had unlimited thrust, infinite amount energy and unlimited time will never reach c.

If you meant what rootone said, then okay i got it.

 

[uumlau]

I think that while the article is technically correct in saying that it would take an infinite amount of energy to accelerate to the speed of light, it's a poor phrasing subject to misinterpretation. You don't even need math to understand why. All you need is the principle of equivalence as applied to electromagnetic phenomena. The math is just a side effect and as I've mentioned elsewhere, the math is not the physics.

Due to the principle of equivalence, no matter how "fast" you go, the speed of light, to you, will still be $c$. If you go even faster, it's still $c$. If you stop, it's still $c$, if you start running backwards, it's still $c$. So saying that it would take"an infinite amount of energy" is misleading, because it suggests that you'd even make a dent in catching up with a beam of light. Yes, other objects might seem to be getting close to $c$, that some kind of extra push might get them faster than $c$, but that's mostly an illusion. In those other objects' frames, photons still travel away from them at $c$, with no chance to catch up at all.

 

[Neandethal00]

Think about it this way: if mass were actually dependent on speed, then an object would have to have an infinite number of different values for its mass, all at the same time, because it has an infinite number of different speeds, depending on the infinite number of reference frames that one can choose to look at it from. Clearly doesn't work.

Shouldn't this be the reason for doubt about interpretations of special relativity? At one point we are saying mass is not dependent on velocity because that would make all objects to have no definite mass. Then we turn around and say mass increases with velocity.

@uumlau: You are using relativistic mechanics to prove certain outcome of relativistic mechanics are wrong. This will never happen.

 

[rootone]

All objects excepting photons (there may be a few others theoretically) have a rest mass and that mass is the same for all identical objects.
Relativistic mass when the object is moving in relation to some frame other than itself is a consequence of mass energy equivalence.
In that case, the moving object has kinetic energy added, the object has greater energy than the non moving object.
Since energy and mass are equivalent in relativity, the object's greater energy can be considered as greater mass.