# Faster than the speed of light

Hi, i'm new to this, so i'm hope this is how this works. But I had a question. I've heard that even theoretically, it is impossible to go faster than the speed of light. Because, even if you provided enough energy to move something faster than the speed of light, i.e using either a lever or a rotational device with 2 extending rods, the speed at which each atom communicate with next moves at the speed of light, so no matter how strong the material is, or how much energy you put, it is not possible to transmit the particles from one to the next fast enough. My question is, is it theoretically possible to increase the speed at which an atom, or even electrons move?

Simon Bridge
Homework Helper
Welcome to PF;
My question is, is it theoretically possible to increase the speed at which an atom, or even electrons move [to faster than light?]?

It would take an infinite amount of energy to accelerate a hypothetical ideal point mass to lightspeed.
But that is not the most serious problem - there is also the matter of causality.

You can, of course, accelerate electrons and atoms to sub-light speeds.

http://www.physicsguy.com/ftl/
... start reading from the introduction.

At the bottom of this page you'll see a section called: "related discussions" - you may want to have a look at those too.

They say that the energy to accelerate to the speed of light is infinite but that is you have the speed of light - the velocity in the denominator so to get the energy your dividing by zero in the denominator so the energy has to go to all infinity. I do not think they have any real particle examples of anything going that fast. It is relative as anything 14 billion years away is traveling at the speed of light already as a function of the universe expanding. Also in communications these days they think that entangled particles can communicate information between themselves at many times the speed of light, theoretically infinite speed.

Also in communications these days they think that entangled particles can communicate information between themselves at many times the speed of light, theoretically infinite speed.

I know this isn't the QM section, but I just want to point out that the entanglement does not seem to be constrained by the speed of light, but the transmission of information is. Locally, anything that could cause something to happen (including information) is constrained by the speed of light.

To daDragon, it does not matter whether you are trying to accelerate an electron or an elephant. Neither will be able to travel at the speed of light in any frame of ref. There are a number of explanations for this. One is the idea that the energy increases without bound as ##v## approaches ##c##. That might be easier to imagine than SB's note about causality.

Simon Bridge
Homework Helper

You brief run-through of various FTL examples seems garbled and barely coherent to me, but at heart I suspect you are questioning the experimental basis for special relativity when you say:
I do not think they have any real particle examples of anything going that fast.
I don't know who "they" are, but the scientific cimmunity does have many real-particle examples which are very close to lightspeed indeed - though there is only one class going at lightspeed and none at all faster. Please see the following list of the experimental basis for special relativity-
http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html
... for some of the experiments that have been conducted.

It is a routine experiment, for example, to accelerate particles such as electrons and protons to different speeds with different energies ... plotting a graph of energy vs speed confirms the special relativity relationship.

I don't know how fast you mean by "going that fast" but - the fastest particle recorded was a proton from cosmic rays:
http://www.fourmilab.ch/documents/ohmygodpart.html/
... managed 0.9999999999999999999999951c. Fast enough for ya?

But there are ways to have an FTL experience besides the examples in post #1.

Riding the expansion of the Universe is one way. This is a geometric/coordinate expansion, and it's details are covered by general relativity. There are other examples.

- you can shine a spot of light on a distant surface: a small rotation of the light source produces a big movement in the spot. You can easily find the geometry which allows the spot to move faster than light across the surface.

- if two objects travel in opposite directions at 0.75c, in the lab, then their separation increases at 1.5c when also measured in the lab.

... both of these are simpler examples of the geometric "exception" to the no-FTL rule.
These are allowed because the rule, in it's simplest form, is that all observers measure the same value for the speed of light in a vacuum.

Entanglement, and non-locality, is another kettle of piranhas though.
http://curious.astro.cornell.edu/question.php?number=612 [Broken]
... tldr: in an entanglement experiment nothing actually travels.
popular reports of ftl communication are exaggerated and misleading.
(Unfortunately the example given is a hidden variables example, which is not quite the same thing, but it does illustrate how you can know two things across vast distances instantly without violating relativity.)

I think that, before trying to discuss the advanced concepts, you really need to get the basics down. Please read the FAQ. It's accessible and contains useful tools to help you talk about relativity issues in a clear way.

Cheers :)

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WannabeNewton
Also in communications these days they think that entangled particles can communicate information between themselves at many times the speed of light, theoretically infinite speed.

This is a gross misrepresentation of quantum entanglement. At the simplest level, all quantum entanglement results from is the existence of state vectors in the tensor product Hilbert space of a two component system that cannot be written as the tensor product of state vectors belonging to the Hilbert spaces of the individual components of the two component system but rather only as linear combinations of such products. The standard spin correlation measurements do not imply any kind of information transfer.

It is a routine experiment, for example, to accelerate particles such as electrons and protons to different speeds with different energies ... plotting a graph of energy vs speed confirms the special relativity relationship.

... The standard spin correlation measurements do not imply any kind of information transfer.

Agreed ... in order to illustrate your comment, I refer to Gell-Mann's book: "The Quark and the Jaguar" (http://www.amazon.com/dp/0805072535/?tag=pfamazon01-20)

Gell-Mann said:
The situation is like that of Bertlmann's socks, described by
John Bell in one of his papers. Bertlmann is a mathematician who
always wears one pink and one green sock. If you see just one of
his feet and spot a green sock, you know immediately that his other
foot sports a pink sock. Yet no signal is propagated from one foot
to the other. Likewise no signal passes from one photon to the other
in the experiment that con rms quantum mechanics. No action at a
distance takes place

I don't know how fast you mean by "going that fast" but - the fastest particle recorded was a proton from cosmic rays:
http://www.fourmilab.ch/documents/ohmygodpart.html/
... managed 0.9999999999999999999999951c. Fast enough for ya?
:)

Well I did go that Faster Than Light website you referred me to and it was interesting, scissors are faster than light in their closing speed. I agree.

I apologize that when I said that I don't think that they have any real particle examples of anything going that fast, that was not what I meant to say. I meant there were no real nearby objects like rocks that were traveling close enough to the speed of light that they could tell what kind of momentum it had and how well that conformed to special relativity. I do not know that the theory will not break down at high energy. For one thing it is said that nothing can escape a blackhole and I am wondering why that is as if something had infinite momentum but it was being held at zero position so the force to hold it was infinite, you would get infinity/infinity = 1, so is that situation was possible. Maybe the discontinuity can be plugged, and at a speed the force needed to increase the speed will not increase so much, kind of like exceeding the speed of sound.

Simon Bridge
Homework Helper
Jedi_Sawyer said:
I meant there were no real nearby objects like rocks that were traveling close enough to the speed of light that they could tell what kind of momentum it had and how well that conformed to special relativity.
That link I gave you about experimental basis for relativity? That has experiments in it that use macroscopic objects going fast enough for relativistic effects to be measured.
eg. the Hafeely-Keeting experiment used a jet aircraft and atomic clocks.

relativity is needed for GPS positioning systems to work:
http://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System

If special relativity works for electrons, neutrons, and protons, then it will work for objects composed of them.
There are engineering problems with accelerating something macroscopic to near light-speed - but there is no reason to believe that relativity does not apply to things like apples and automobiles in the same way they apply to atoms and stars.

it is said that nothing can escape a blackhole and I am wondering why that is as if something had infinite momentum but it was being held at zero position so the force to hold it was infinite, you would get infinity/infinity = 1
1. infinity does not work like that - google for "cantor". In fact - "force" does not work like that either - please review Newtons Laws of motion for the classical definition. Force is a bit trickier in relativity... please make sure you understand forces before using force arguments.
2. even things did work like you described - that still would not represent an object escaping a black hole - that would be an object requiring an infinite force to remain at a constant altitude: which is what people normally mean when they say "nothing escapes".
3. beware of pop-science - it is incomplete and more poetic than accurate.

What you seem to be saying with all this is that if something has not been directly measured in some circumstances then maybe the theory does not hold in those circumstances? i.e. it is not possible to confirm general theories from specific examples. If so then your problem is that your personal philosophy is at odds with the philosophy of science and you need a different forum for your questions.

Also see:
http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html

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Simon Bridge
Homework Helper
me said:
...plotting a graph of energy vs speed confirms the special relativity relationship.
... what is it about the statement that you don't understand?

See: http://en.wikipedia.org/wiki/Tests_of_relativistic_energy_and_momentum - for an overview to help you refine the question.

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http://www.fourmilab.ch/documents/ohmygodpart.html/
... managed 0.9999999999999999999999951c. Fast enough for ya?

The most amazing part about that velocity is not its closeness to the speed of light but the precision to which it is known. When the velocity is known to such precision it means that the position must be smeared over a significant distance. In such a case a particle detector may actually detect the particle ahead of its mean position giving a result in which the particle appears to be travelling faster than light.

UltrafastPED
Gold Member
The most amazing part about that velocity is not its closeness to the speed of light but the precision to which it is known. When the velocity is known to such precision it means that the position must be smeared over a significant distance. In such a case a particle detector may actually detect the particle ahead of its mean position giving a result in which the particle appears to be travelling faster than light.

They are not measuring the speed; they measure the energy content, determine the Lorentz factor, which is the ratio of the energy measured/rest energy, then back-out the speed.

So your concern would be the accuracy of the energy measurement ... but this only changes the Lorentz factor, and no matter what the Lorentz factor is you will always obtain a speed less than c.

Simon Bridge
Homework Helper
##\renewcommand{\E}[1]{\langle #1 \rangle}##
skeptic2 said:
In such a case a particle detector may actually detect the particle ahead of its mean position giving a result in which the particle appears to be travelling faster than light.
... leaving aside that the actual example was not done that way;

It's difficult to figure what you mean. It's quite a ticklish area to talk about so you have to get very very precise and careful with your wording. Which really means you need math ...

For example:
One could set up an experiment where a single particle leaves the source at t=t1 and gets detected some distance d away at t=t2, then the speed determined by v=d/(t2-t1) may show v>c as an artifact of the experiment if the uncertainty in v is quite high ... but you are talking about the case where the uncertainty in v is low!!

i.e. you seem to be saying that if the precision in measuring v is high then the possible variation is high - maybe high enough that v > c as an artifact of this variation?

Looking at it another way:

Same experiment:
Classically, the particle position is the expectation value of the position wavefunction <x> and it's velocity, the bit that follows Newton's laws for eg. is the group velocity of the wave <vg> (a deBroglie hypothesis).

Note: We may want rather ##\bar v = \frac{d}{dt}\E{x}## as the classical velocity, since the group velocity can do odd things... we certainly prefer energy and momentum measurements to velocity. Avoids ambiguity. Anyway...

But since the wavefunction is spread out in space, there is a small chance of detecting the particle ahead of the time ##\small{\Delta t = d/\E{vg}}## or ##\small{\Delta t=d/\bar v}##. If the spacial spread is very large, then there is a chance that d/Δt > c.

If this is more like what you are thinking of, then you may want to see:

I think both of these pretty much deserve their own threads though.
This is why so many people prefer the "communication" form of the "lightspeed limit".

Simon Bridge you mentioned that GPS needed to take into effect relativity effects, I know they think they know compare timing signals to solve the simultaneous equations to determine where they are if that is what you mean.

I believe that for GPS they were claiming precision that they found out that they did not have. I forget where but approx. 5 years ago I saw an article that the Army had been claiming a precision of 30 centimeters on GPS tracking, it turned out that they had to be in their special test area to get that accuracy. When they expanded the range they were getting readings that were between 40 cm to more than a meter off, they also had some variability due to receivers they were using.

Simon Bridge
Homework Helper
What sort of precision the army once thought or did not think they had is besides the point.
By your own "belief" the army had that level of precision in their test area... precision achieved in that area would have included relativistic corrections without which the timings would produce a systematic error that increases with time.

There is now a great deal of data on GPS positioning and a lot of satellites are involved.
The data is great because it can be checked by anyone with a GPS receiver.
But even if you throw out all of that, there still remains the other examples mentioned here and the great many others in the links from this thread so I wonder what your point is supposed to be?

What you seem to be saying with all this is that if something has not been directly measured in some circumstances then maybe the theory does not hold in those circumstances? i.e. it is not possible to confirm general theories from specific examples. If so then your problem is that your personal philosophy is at odds with the philosophy of science and you need a different forum for your questions.

Anyway: you have this bad habit of referring to "they said" and "I read something" and so on.
I don't normally respond to that kind of rumor and innuendo: who said it and where did you read it?
You will benefit most from a bit more work substantiating your beliefs rater than me answering endless niggles.

You'll find a lot of your doubts will be answered when you start using citations.

i.e.
... relativity in GPS systems

http://en.cnki.com.cn/Article_en/CJFDTOTAL-ZGMT200603022.htm
... reliability analysis

Simon, got it, my word and $5 will get me a cup of coffee, ok. You are the one that brought GPS was some sort of proof that the relativity theory holds at high energy and momentums, which is what I was questioning. Everybody knows that light is relative. why mention it in the context of what I was questioning, I went to your citations above. The first reference you quoted above is a 42 page document and if there is something in it that you think particularly proves the theory of relativity at high energy that momentum goes to all infinity, usually a sign a theory needs adjustment, tell me exactly what it is and where in the document I could find it. The second reference was a useless page called "The Way and Reliability Analysis of GPS Height Fitting" and that had a one paragraph description of what another link would get you to. Try to open that and you get to a Chinese sign in page, (only one of the two links worked) In short if you have to include citations will you make them relevant and don't waste peoples time trying to figure out why you included them and what in these references is worth reading. Simon Bridge Science Advisor Homework Helper Simon, got it, my word and$5 will get me a cup of coffee, ok.

You are the one that brought GPS was some sort of proof that the relativity theory holds at high energy and momentums, which is what I was questioning.
I hoped that GPS was one example among many of a macroscopic low energy system where relativistic effects are important ... my assertion is that you don't need to have direct measurement of a macroscopic scale object at high relative velocity to prove the validity of special relativity.

I think there is a misunderstanding here. Nothing will prove relativity.
Nobody is trying to prove it. It is not possible. That help you?

The best we can manage is to confirm the theory.
If the theory is confirmed for electrons, protons and neutrons, it is also confirmed for baseballs and rocks.

Everybody knows that light is relative.
On the contrary - light is not relative. That is one of the fundamental postulates of special relativity.

... why mention it in the context of what I was questioning,
<checking> Because you asked a question for which the mention appeared to be a valid response?
Or did you only want examples that were obscure?

I went to your citations above. The first reference you quoted above is a 42 page document and if there is something in it that you think particularly proves the theory of relativity at high energy that momentum goes to all infinity, usually a sign a theory needs adjustment, tell me exactly what it is and where in the document I could find it.
I didn't - one reference was to show the validity of time-dilation corrections in GPS data, and the other is to show how special relativity is used to improve the accuracy of distance calculations - in this case, height.
Each of those were questioned by you in a previous post... I was not sure what your point was and so far you are not forthcoming with it.

Note: the chinese research stuff seems to have stopped working all right. Don't know why.
(For me - it is taking forever to lead.)

No matter - the relativistic corrections to gps are now text-book stuff:
... that should work better: it is a discussion of how the corrections are made and used.

Is it your claim then that the relations of special relativity remain untested by experiment for some circumstances? Well probably. I doubt anyone has tested them for, say, basket-balls. But my response is: so what?

What you seem to be saying with all this is that if something has not been directly measured in some circumstances then maybe the theory does not hold in those circumstances? i.e. it is not possible to confirm general theories from specific examples. If so then your problem is that your personal philosophy is at odds with the philosophy of science and you need a different forum for your questions.

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ZapperZ
Staff Emeritus