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

[en_pris]

One of the definitions of mass is resistance to acceleration. When it is said that mass increases, understand this statement in the context of this definition. Accelerating towards light speed relative to a particular inertial frame requires more and more energy per unit of velocity added the closer to light speed one gets.
However, there is a much more serious limitation that occurs at speeds even less than 1% of light speed, and that is encountering debris in space.
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At what speed does the interstellar medium become lethal to high speed flight? This is an important consideration if interstellar travel is to become a reality for mankind. The nearest star is over 4 light years away. Even 1 light year is an immense distance by human standards, requiring a travel time of 20,000 years at shuttle speeds. So an investigation into travel at higher velocities becomes appropriate. However, at higher velocities, encounter with debris in the interstellar medium must be considered.
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We don't really know what the interstellar medium looks like. If it is just stray hydrogen atoms you will experience a head-on flow of cosmic rays that will collide with your spacecraft and probably generate secondary radiation in the skin of your vehicle. This can be annoying, but it can be shielded so long as your speed is not near light speed. At speeds of 50 to 90% light speed, these particles are not likely to be a real problem. At speeds just below the speed of light (e.g., 99%), the particles would generate a very large x-ray and gamma-ray background in the skin of your ship. Significant shielding will be necessary to protect the crew and instruments.
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As it turns out, our solar system is inside a region called the Local Bubble, where the density of hydrogen atoms is about 1% of that in the general interstellar medium. This bubble, probably produced by an ancient supernova, extends about 300 light years from the Sun. There are thousands of stars within this region. Hydrogen atoms in interstellar space should not be a hazard while exploring the Local Bubble.
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Interstellar space also contains a few microscopic dust grains (micron-sized: 1 micron = 1 millionth meter) in a cube about a few meters on a side. At their expected densities, you are probably in for a rough ride, but it really depends on your speed. The space shuttle, encountering flecks of paint traveling at 28000 mph (0.005% light speed) is pitted and pierced by these particles, but dust grains have mass a thousand times smaller than the smallest paint fleck, so at 0.005% light speed, dust will not be a problem. However, if you want to travel even to the nearest star in a reasonable time, say in 8 to 10 years, 50% light speed will be required. Your likelihood of encountering a large dust grain at high speeds becomes significant. Only one such impact would be enough to damage your vehicle beyond repair given the energy involved. An example:
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A large dust grain may have a mass of a few milligrams. Consider the kinetic energy of a dust grain weighing just one milligram (0.001 gram) at 0.5% light speed:
KE = 0.5mv^2 = 0.5x0.001 gram x (0.5x3x10^10 cm/sec)^2 = 1.125x10^17 ergs.
This is the kinetic energy of a 10 gram bullet traveling at a speed of 1500 KILOMETERS (not meters) per second, a million times the energy that such a bullet would normally have (kinetic energy is proportional to the SQUARE of velocity). The point is, at these speeds even a dust grain would explode into an intense fireball that would melt through the skin of any vehicle. 1500 Kilometers per second is just 1/2 of 1% the speed of light. At that speed it would take 800 years for a one-way trip to the nearest star. Your likelihood of encountering such a dust grain is dependent on the volume of space your vehicle sweeps out, and the density of such dust grains. For those interested, NASA has made available a website containing a tool that will calculate the cosmic-ray transport and diffuse emission production resulting from interstellar dust grains in the Local Bubble. Check out http://galprop.stanford.edu/webrun.php and register as a user. This website requires you to show an "affiliation". However, the interstellar medium probably contains ice globules from ancient comets. Impacts with these objects even at 1/10 of 1% of light speed would be fatal. Discovering the size distribution of debris in interstellar space becomes essential in determining the survivability of vehicles.
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The conclusion is that with any technology we can reasonably imagine, interstellar travel near light speeds is not only difficult but most likely not feasible. This leaves us with cryogenics or generation ships as possibilities for methods of interstellar travel at speeds much slower than light speed, that is, until someone discovers how to warp space.

 

[thetexan]

I guess I'm having the same problem in understanding as most people who try to grasp the concept of limited velocity. Let me see if I can explain my confusion.

I know that the entire concept of velocity requires a comparison of one thing to another. When I say I am going so fast, I expect you to relate that in terms that is meaningful to you, which means in your frame of reference. I get that. This means that velocity can not be measured without first stipulating against what we are measuring the velocity.

I guess I'm speaking of a theoretical thought experiment type of velocity.

If I accelerate at 1 g forever and I calculate the velocity, at least in my mind I will eventually surpass c. If I am in a spaceship with all the windows closed all I can go on is the accelerometer and the clock. Both of these instruments, in my frame of reference are working normally and so I can calculate the velocity. It has been said in previous posts that I can continuously accelerate forever. So let's say I calculate my velocity at 5c. Now I open one of my windows and look at a star and measure my velocity and discover I'm only going near c, not more than c and certainly not the calculated 5c.

In my thought experiment, I'm concluding that in my frame of reference I can actually travel more than c but when I try to relate that to any other frame of reference I can not.

That seems to suggest that the problem is not in the velocity itself but in the measuring of the velocity at or near light speed.

So here is one question that may help me better understand. What came first the chicken or the egg? Since we cannot measure velocity beyond c do we conclude that there is no velocity beyond c? Or, Do we know there can not be a velocity beyond c and therefore that is why we can't measure anything beyond c?

It seems curious to me that the common aspect to this is light and it's speed. We taste with chemical transactions, we smell with odors, another chemical transaction, we hear with sound waves, we feel with stimulation of nerves, and we see with light waves. Of the five, light is the fastest available transmitter of information. The very information we need to make a measurement of velocity, especially near light speed. Doesn't it seem that this limitation of speed for the transmission of the information needed to measure one thing's velocity against another in any particular frame of reference would dictate how that measurement could be made and would be the limiting factor in what we could ever conclude about the speed of the thing measured?

Here is another thought experiment question. What if the speed of light was found to be actually 300,000 mps rather than 186,282. Would we not then say that the fastest velocity (the very use of the word velocity means a comparative measurement between two objects in a particular frame of reference) we could observe is 300,000 mps? And wouldn't the reason be because no faster velocity's information can be transmitted faster than 300,000 mps. In other words, isn't the choke point the information transmission speed (that of light itself) rather than the actual velocity of the object?

An analogy here might help explain my thought. Imagine I am in the stands at an airshow with my wife and a jet crosses right to left in front of the crowd at near the speed of sound. I blindfold myself and she doesn't. Both of us point to the plane as it passes. My observation is limited by the speed of sound since that is the fastest transmitter of information I have available to me. Her observation is limited by the speed of light since that is the fastest transmitter of information she has available to her.

As the plane passes I point where I hear the plane which is a quarter mile behind where the plane actually is. She points to where the plane actually is. The reason for the discrepancy is due to the differences in speed for the transmission of information regarding the location of the plane. When I have used this analogy before I get the discussion that sound travels through a medium and light doesn't. This misses my point entirely. My point is that, for whatever reason, the information used to measure the speed or position of something is dependent on the ultimate velocity of the system used to transfer the information used to make the measurement and, to me, seems independent of the actual velocity of the thing itself. In my example it doesn't matter at what speed the plane passes I will always point to where I hear the sound which will only get to me at the speed of sound. No matter what the pilot does or how hard he tries or how fast he flies, he can never convince me he is traveling faster than what I perceive he is by listening to the sound. He knows he's going faster but he can't convince me. My perception is limited by the limit of the velocity of the thing that transmits the information about the plane to me, sound. In fact, I will swear to my dying day that nothing can go faster than the speed of sound. All the while arguing with my wife who claims the plane was actually traveling at mach 3. Again, this has nothing to do with the medium in which sound travels compared to light. This is an illustration of the difference between the velocities of two different transmitters of information, and our perception's dependence on that velocity to make measurements.

What if we, in a thought experiment, had a faster transmitter of information. Say, thought transference, for example. Let's say the speed of thought transference was experimentally measured at 20 times the speed of light? Then would we say that the fastest velocity attainable was the speed of thought? And would that be because there was an actual limit to velocity itself, or just a limit to the velocity of thought which transmits the information about velocity?

I can never get a clear answer to whether we KNOW that we KNOW whether there is a limit to actual velocity or just that its measurement is limited by the speed of of the transmitter of the information (light) used to make the measurement and therefore we cannot say, other than to conclude there is no faster speed.

Believe me when I say that I enjoy studying subject and have truly tried to grasp the concepts. I just still have nagging questions. That's why I turn to smart guys like you all.

tex

 

[phinds]

In my thought experiment, I'm concluding that in my frame of reference I can actually travel more than c but when I try to relate that to any other frame of reference I can not.

Could be that's your problem. In your own frame of reference you are always motionless.

 

[thetexan]

Possibly. Except that I do feel the acceleration and that is confirmed by the accelerometer.

 

[phinds]

Possibly. Except that I do feel the acceleration and that is confirmed by the accelerometer.

It's not "possibly". I did not state that as a matter of personal opinion, I stated it as a physical fact. And what does your acceleration have to do with how you see your clock? (hint: nothing at all).

 

[rootone]

Yes, Tex is obviously not in motion relative to himself, but I am curious on that point made about 'feeling the acceleration', (and that the use an instrument to verify it)
He should be experiencing some level of g force all the time whilst the engines are being fired, thus he can conclude that he is accelerating, at least in relation to his previous position.
However since c cannot be attained what actually happens here?, will he feel a lot less g force and and eventually very little at all, despite the fact that his engines are reliably continuing to provide thrust?

 

[DaveC426913]

He should be experiencing some level of g force all the time whilst the engines are being fired, thus he can conclude that he is accelerating, at least in relation to his previous position.

True.

However since c cannot be attained what actually happens here?, will he feel a lot less g force and and eventually very little at all, despite the fact that his engines are reliably continuing to provide thrust?

No. He will feel a constant force against his feet.

The question is: why are you correlating the force at his feet with his velocity? The force does not tell you the value of some absolute velocity, especially when you know full well that velocity is meaningless without comparison to some external reference point.

The answer is that you are assuming that constant acceleration will result in a proportionate increase in velocity with respect to some external reference.

 

[DaveC426913]

Could be that's your problem. In your own frame of reference you are always motionless.

Possibly. Except that I do feel the acceleration and that is confirmed by the accelerometer.

All the accelerometer can show is that you are experiencing a net force. Inside your spaceship, you cannot conclude by observation that this force is acceleration. The Principle of Equivalence states that acceleration and gravity are locally indistinguishable, meaning your experiments are telling you that you are either stationary on the launch pad on Earth, or accelerating at one g.

 

[phinds]

And texan, just to be sure you are clear about the ramifications of Dave's post, regardless of whether you are accelerating or not, you are still always motionless in your own frame of reference.

 

[rootone]

The answer is that you are assuming that constant acceleration will result in a proportionate increase in velocity with respect to some external reference.

OK, just about got my head around that, thanks.

 

[russ_watters]

Submarines use inertial navigation systems that work in the way being described. The same systems would not work at high speeds unless relativistic corrections were applied.

There is nothing you would feel that would be any different, but if you look out your window you would see that your INS has you in the wrong location.

Roughly, if you took off from Earth and accelerated at 1G, for a few months everything would be fine. But after 3.5 years, you'd pass Alpha Centuari at just under the speed of light, while your INS says you are traveling three times the speed of light and passed it a year ago.

 

[thetexan]

Yes, the principle of equivalence says it COULD be acceleration or it COULD be gravity, I can't know, or better stated, I can't know unless I have evidence showing which it is. Just because the man in the elevator can't tell whether his feeling of heaviness as the elevator accelerates upward is from the acceleration or gravity doesn't mean with other evidence he can't deduce which it is. But, here, I am stipulating that it IS acceleration. I am in intergalactic space thousands of light years from anything mass that could create a 1 g acceleration. My engines are running and and the telemetry from the engines and the known mass of the spacecraft gives me clear evidence that it IS acceleration I am feeling. So I must be going faster and faster. I can at least say that I am going faster than I was a minute ago, and the minute before that, etc.

I'm having a hard time with the logic of this...that because we can't say for sure whether the acceleration is gravity or true acceleration therefore we must conclude that it is not acceleration and therefore velocity can not possibly be increasing as a result. If there were no heavenly bodies at all, and I had no exterior reference to prove I was even moving, the very fact that I see engines pushing and feel an acceleration must mean that I am moving.


"The answer is that you are assuming that constant acceleration will result in a proportionate increase in velocity with respect to some external reference."

Not yet I'm not. I'm still in my thought experiment in a ship with no windows and no external reference...yet. I don't need an external reference to know I am accelerating because I am stipulating that the effects are from the acceleration from the engines back there rather than gravity. Engines are burning and I have an indication on the accelerometer. If I tell the guy in the elevator that I am about to start the elevator up then he is right to conclude that what he feels is not increased gravity even though the effects are the same and feel the same. He knows which one it is.

I have a hard time with the argument that it is impossible to tell which it is acceleration or gravity when you have information that indicates which it is. I don't understand that it is necessarily impossible to gather enough evidence in your own frame of reference to indicate which is causing the effect. Even if it is impossible to tell under any circumstances you would still have to allow for an explanation for each of the two possibilities. Just like the equation y=x^2. It could be one of two possibilities but we graph both because either is possible. The fact the 9 could be the result of -3 or 3 and that I don't know which doesn't mean I have to operate or postulate as if it can't be either or that either is knowable. It might be gravity...then again...it might be acceleration. What if it is acceleration? Actually. Then we know we must be moving and if so, then what limits the velocity? I know that one's ability to measure a velocity is limited to that of c. Does that prove that the limitation on the measurement also limits velocity?

Is it possible that it's not the velocity that's limited (as I analogized with the super sonic plane) but rather the ability to measure the velocity beyond that of c?

In my frame of reference, I calculate that after 10 years of running my engines at a constant 1 g acceleration that I must be going some phenomenal speed. Maybe even hyper c. I can't PROVE it to you but I know I am. The most anyone can PROVE is that I am close to c because then we have to take external reference frames into consideration as part of the proving process. I will never be able to prove I went faster than light, but I know I did.

I know guys like me with an amateurish understanding of this complicated subject must be frustrating to talk to. I am sorry for that.

But then I think this...What if I lock myself up in my ship, turn on the engines and accelerate to what I believe is 5c and point toward some distant star. If I am actually traveling at 5c I should arrive at the star in 1/5th the time I would if I was going 1c. So eventually I look out the front window and discover I'm no closer than I would have been at 1c. My calculation for 5c was either wrong, the acceleration I calculated didn't add up to 5c, or the star is not where I think it is. It could be that it is really closer (as if 5c) but the light from it hasn't got to me yet because it is limited to 1c. Assuming the possiblity that my calculations were correct and that I was really traveling at 5c I would have to take that into account when deciding when to stop so I don't plow into a star I can't see yet. Here's the problem. I stop short of the star thinking it must actually be right in front of me (as if 5c) but it seems far away (as if 1c). If that is true then it will take another several years for the light to catch up with where it really is. So I will have to wait all of that time as the star (actually star light) comes closer and closer to me. After a few years I will find out the final result of my calculations. So, again, what was the use of getting there fast if I have to wait to know if I've actually arrived? My head hurts.

Warp drive is the key.

Just like if I were to try to cross a street blindfolded based on where I hear the speeding car is. I better take into account that my perception is limited by the speed of sound and calculate accordingly.

I'm not arguing with anyone. I just find this facinating and enjoy talking about it. My dad and I used to talk about this when I was a kid.

tex

 

[DaveC426913]

Yes, the principle of equivalence says it COULD be acceleration or it COULD be gravity, I can't know, or better stated, I can't know unless I have evidence showing which it is

What if you looked out the window and discovered that your engines were on but that you were hovering 100 feet above the launchpad the whole time? You've been experiencing 1g the whole time, yet - and here's the kicker - your velocity has not increased at all.

So...

So I must be going faster and faster. I can at least say that I am going faster than I was a minute ago, and the minute before that, etc.

... can you?

In my frame of reference, I calculate that after 10 years of running my engines at a constant 1 g acceleration that I must be going some phenomenal speed. Maybe even hyper c.

Only if you used a Newtonian calculator, and ignored the very real effects of relativistic time dilation. You would literally be doing the calculations wrong.

It is known (observed) that, approaching c, time dilation becomes significant, meaning all that acceleration you were doing is being stretched over a longer and longer period of (external) time. You would not be accounting for that.

But then I think this...What if I lock myself up in my ship, turn on the engines and accelerate to what I believe is 5c and point toward some distant star. If I am actually traveling at 5c I should arrive at the star in 1/5th the time I would if I was going 1c. So eventually I look out the front window and discover I'm no closer than I would have been at 1c. My calculation for 5c was either wrong, the acceleration I calculated didn't add up to 5c, or the star is not where I think it is. It is really closer (as if 5c) but the light from it hasn't got to me yet because it is limited to 1c. Assuming the possiblity that my calculations were correct and that I was really traveling at 5c I would have to take that into account when deciding when to stop so I don't plow into a star I can't see yet.

Actually, what would happen is that, looking out the window, you would find yourself having arrived at the star, which - due to relativistic length contraction - would be five times closer than you had measured it from Earth. The star would be approaching you at very close to c, and Earth would be receding from you at very close to c. Of course, when you made landfall, you'd discover that 5 years had passed since you left Earth.

The whole galaxy, ahead and behind you, would be squashed to 1/5th its expected diameter. If you continued to accelerate, you could eventually leave our galaxy and make it some distance way to Andromeda. Its distance would have shrunk from 2 million light years to a mere 400,000 light years by the time you passed your star, and would continue to shrink as you continued to accelerate toward it. You could shrink that distance to 50 light years and get there in your lifetime, but 21st century Earth would be long gone by millions of years.

 

[thetexan]

Dave, you're a good man.

 

[phinds]

Dave, you're a good man.

Oh, don't encourage him, it always goes to his head

 

[rogerthat1945]

Basically: In an infinite universe; you are never moving, anywhere: You are only ever moving in relation to some object near you. So, you can measure the speed of light against that. And if you are traveling in the opposite direction of something traveling half the speed of light, and you are traveling at the same speed; then you will see whatever you think you will `see`.

 

[phinds]

Basically: In an infinite universe; you are never moving, anywhere: You are only ever moving in relation to some object near you.

That's true but it does NOT require an infinite universe for it to be true.

So, you can measure the speed of light against that.

unnecessary. Since the speed of light is the same in all frames, it doesn't matter what you measure it against

And if you are traveling in the opposite direction of something traveling half the speed of light, and you are traveling at the same speed; then you will see whatever you think you will `see`.

HUH? This makes no sense.

EDIT: it occurs to me that perhaps you do not understand relativistic velocities and how they add. Google "Lorentz Transform" for more information.

 

[uumlau]

a question has made my mind busy...it is told that there is no frictions at space...frictions of air...friction of gravity and etc...none of these does exist in the space (outside the earth)...so we can launch a spacecraft with a primary speed(orbit speed of earth) and equip it with a engine...with a primary speed , and with a engine , and without any friction...theorically we can increase the speed and acceleration...and then reach to a ultra high speed until a speed like light speed...but WHAT IS THE LIMITATIONS?

The limitation is that on your almost-light-speed ship, if you aim a flashlight in the direction you are going, the light doesn't ooze forth in a slow-motion way. It's still going LIGHT SPEED!

Yes, you should be thinking "What the ... ??" about now.

The overall rule that Einstein posited and has been verified over and over is that no matter where you are or how you are moving, the speed of light (in a vacuum) is always measured to be the same speed. Always and everywhere. If it didn't, there would be all sorts of consequences to electromagnetic behavior that simply don't happen.

Why is this true? We don't know. That's a philosophical question. We know that it IS true.

The universe "moves the goalposts" if you will. You can go however fast you want, but photons will always be moving at the constant speed of light with respect to you. The weird math of special relativity is the result of what else has to be true in order for all those photons to have the same speed to everyone else, too.

No, it's impossible to REACH it, not just go past it.

In classical terms, this is true. In quantum terms, the truth is a bit fuzzier. Very roughly speaking, an electron moving near the speed of light (relative to us) has a very small probability to be measured as going faster than light, which implies that there exists a reference frame in which it is going "backwards in time", in which case it would appear to be a "positron", the antimatter version of an electron. More precisely, the Dirac equation handles these relativistic cases, which is how he predicted antimatter. http://en.wikipedia.org/wiki/Dirac_equation

 

[Drakkith]

In classical terms, this is true. In quantum terms, the truth is a bit fuzzier. Very roughly speaking, an electron moving near the speed of light (relative to us) has a very small probability to be measured as going faster than light, which implies that there exists a reference frame in which it is going "backwards in time", in which case it would appear to be a "positron", the antimatter version of an electron. More precisely, the Dirac equation handles these relativistic cases, which is how he predicted antimatter. http://en.wikipedia.org/wiki/Dirac_equation

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.

 

[DaveC426913]

Very roughly speaking, an electron moving near the speed of light (relative to us) has a very small probability to be measured as going faster than light,

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.

So your statement is more correctly:

An electron moving near the speed of light (relative to us) has a very small probability to be measured as going even closer to the speed of light.

 

[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.