Particles with mass can't reach speed of light?

[SpiderET]

One of the important predictions of relativity theory is that particles with mass can't reach speed of light in vacuum and will always be slightly slower.

I wanted to know more about the maximum speed which can be reached by particles with mass and looked for relevant experiments. But to my surprise, there was no difference experimentally confirmed. Within experimental error, particles with mass are reaching speed of light. This is especially valid for neutrino, which is particle with confirmed mass and with several experiments measuring the speed of neutrinos. And with each experiment, result of neutrinos reaching speed of light is confirmed with better and better precision. Latest experiment confirmed it at the level of 10 -19, so there is extremely small margin left for the predicted difference in speed.

https://en.wikipedia.org/wiki/Measurements_of_neutrino_speed

This can't be regarded as falsification of relativity theory, but it seems to me, that there is missing experimental proof or astronomical observation for one of the most important predictions of relativity theory. I wonder if somebody else here knows better about this topic.

 

[russ_watters]

Particle accelerators provide very good evidence in support of the speed limit. Also note that while neutrinos can't yet be confirmed to travel below C, they are at least, confirmed to not travel much above C, implying C is the limit.

 

[Orodruin]

To add to what russ said: Neutrino masses are tiny. There is no reason to believe that we should have seen the deviation from the speed of light, given the energies of the neutrinos we have observed. Therefore, the results are very consistent with the predictions of relativity.

 

[SpiderET]

To add to what russ said: Neutrino masses are tiny. There is no reason to believe that we should have seen the deviation from the speed of light, given the energies of the neutrinos we have observed. Therefore, the results are very consistent with the predictions of relativity.

Thanks for reply. I haven't found some specific calculations or experiments, but given we know the mass of neutrino, I wonder if the theoretically predicted difference in speed is within experiment error level or we already should have seen the difference in results of some experiment. That would be interesting situation.

 

[ZapperZ]

And if anything, the OPERA debacle strengthened the principal that neutrinos are not superluminal.

I think that there is nitpicking going on in the OP. In many cases, it is a simplification to use c as the speed of these almost-massless particles. When we deal with neutrinos and relativistic electrons, we can simply use c as their speeds without losing a lot of accuracy in our calculations. After all, the difference between 0.99999c and c often does not show up in many calculation that matters.

Zz.

 

[Orodruin]

but given we know the mass of neutrino

We don't. We actually only have an upper limit and mass squared differences, which means that the lightest neutrino technically could be massless.

I wonder if the theoretically predicted difference in speed is within experiment error level or we already should have seen the difference in results of some experiment.

But I just told you we should not have seen it yet ...

 

[SpiderET]

And if anything, the OPERA debacle strengthened the principal that neutrinos are not superluminal.

I think that there is nitpicking going on in the OP. In many cases, it is a simplification to use c as the speed of these almost-massless particles. When we deal with neutrinos and relativistic electrons, we can simply use c as their speeds without losing a lot of accuracy in our calculations. After all, the difference between 0.99999c and c often does not show up in many calculation that matters.

Zz.

The question was never about superluminal speed, it was about particles with mass reaching speed of light.

I don't think its nitpicking. Relativity is regarded as perfectly confirmed by experiments, but when I go really into detail in some cases I found out that some important predictions have rather weak experimental confirmation or are not excluding other interpretations. If somebody would propose a theory where all particles, with or without mass can reach speed of light, would be there some experiment which would falsify it? It seems that currently there is no such experiment.

 

[Vanadium 50]

I found out that some important predictions have rather weak experimental confirmation

Sorry, but that is not the case. We have never, ever, seen a particle moving faster than light. It is true that you can go to situations where it is difficult to measure the difference between the speed of a particle and c. But the fact that one can come up with a measurement that is difficult - even too difficult - tells you nothing. We can always come up with hard measurements.

 

[ZapperZ]

The question was never about superluminal speed, it was about particles with mass reaching speed of light.

I don't think its nitpicking. Relativity is regarded as perfectly confirmed by experiments, but when I go really into detail in some cases I found out that some important predictions have rather weak experimental confirmation or are not excluding other interpretations. If somebody would propose a theory where all particles, with or without mass can reach speed of light, would be there some experiment which would falsify it? It seems that currently there is no such experiment.

But read what I had written in later in the post!

I'm an experimentalist. I care about not only accuracy, but also to what extent experiments can and cannot say about something. I can tell you that it is VERY difficult to distinguish between 0.9999c and c. So because I can't distinguish it in my measurement, there is no way I can say one way or the other. All I can say it that c is still the limit since we have no superluminal detection (which is why I brought up OPERA).

But that is actually relevant here because of the theoretical foundation of what it implies. In a direct way, it reconfirms the basic tenets of Special Relativity. Now, unless you are willing to accept SR only in bits and pieces, then you are faced with the idea that (i) c is the ultimate speed limit and (ii) particles with mass can only reach c asymptotically.

Zz.

 

[PAllen]

Throughout history of science, you get types of predictions that would take infinite precision to verify, therefore are unverifiable. To support/reject theories you focus on the predictions that can be verified. An internally consistent theory that is not refuted is acceptable. If there are two such theories making identical predictions for experiments that can be carried out, you can't choose one over the other. However, there is no candidate theory I've ever heard of that says massive particles can travel at exactly the speed of light.

Any prediction of any theory that something has some exact value can be falsified but never verified, because it would require infinite precision. Focusing on this uniquely for SR is silly nit-picking. SR predicts that at appropriate energy, any particle can get as close to c as desired. This is verified to high precision. SR predicts none will exceed c. This could easily be falsified, but hasn't been.

If I claim that the two way speed of light is faster by one part in 10¹⁰⁰ in directions to/from Mecca than other directions, can you disprove it? Would you see any point in entertaining such a proposition with no well defined theory behind it?

 

[SpiderET]

Thanks all for replies, I think I understand the topic much better than before.

 

[Dale]

But to my surprise, there was no difference experimentally confirmed. Within experimental error, particles with mass are reaching speed of light.

Which is what relativity predicts.

 

[russ_watters]

In case you still check back, I'm not sure this was explicitly answered:

Relativity is regarded as perfectly confirmed by experiments...

No scientist would ever claim such a thing. It goes against the scientific method. Indeed, the existence of an error margin is inherrent in all measurements and makes this and every other theory imperfectly confirmed.

...but when I go really into detail in some cases I found out that some important predictions have rather weak experimental confirmation or are not excluding other interpretations. If somebody would propose a theory where all particles, with or without mass can reach speed of light, would be there some experiment which would falsify it? It seems that currently there is no such experiment.

You're not understanding the full implications of what you are suggesting. There are two ways to look at it:
1. The speed of light/universal speed limit is very slightly different from what is currently accepted -- but within the current error margin. If that's the case, then that doesn't mean objects can reach the speed of light, it just means the speed is very slightly - immeasurably - different from it is now. Nothing whatsoever changes about the theory, we just adjust the accepted value slightly.

2. An object with mass could really move at the same speed as light. If that were the case, a new theory would need to be proposed to explain it, but I don't think you realize just how difficult such a theory would be to match current observations. The way Relativity works is very different from Newtonian mechanics: when you apply a constant force to an object in its frame and measure its speed from another frame, you will watch its acceleration decrease asymptotically toward zero but never reach it, while its speed asymptotically increases toward C without ever getting there. It is very difficult, mathematically, to describe a phenomena where an asymptote becomes reached.

Now, while you may think that experimentally the difference here is very small, you're just picking an experiment that doesn't highlight the difference. If instead of speed you looked at kinetic energy, the differences as you approach C become enormous: like mistaking a fly for a freight train.

 

[ohwilleke]

The question was never about superluminal speed, it was about particles with mass reaching speed of light.

I don't think its nitpicking. Relativity is regarded as perfectly confirmed by experiments, but when I go really into detail in some cases I found out that some important predictions have rather weak experimental confirmation or are not excluding other interpretations. If somebody would propose a theory where all particles, with or without mass can reach speed of light, would be there some experiment which would falsify it? It seems that currently there is no such experiment.

To give an example of how we experimentally confirm special relativity; special relativity predicts the time dilation expected of a short lived particle like a muon, as a function of its speed which is in turn a function of its kinetic energy. Muons accelerated with 100 GeV of energy each are going to have a half-life in the reference from of observers at rest in the particle accelerator of X which is much longer than the half-life of a muon not accelerated. The relationship between the energy we use to accelerate a muon and its observed half-life, corresponds closely to the expected value. If the muon were going at exactly the speed of light, however, we would expect the muon to never decay, which is not what we observe, even when we give the muon immense energy boosts. The asymptotic behavior of muon decay rates with respect to energy of acceleration is very powerful evidence that special relativity is true, and if special relativity is true, then massive objects can't actually reach the speed of light.

It turns out to be much easier to measure the energy of acceleration and the decay rates with minimal systemic error, than it is to measure speed itself, because at high energies the marginal increase in velocity from an increase in energy is so small. As energies get higher relative to particle mass, the difference between "c" and the particle's speed in your reference frame becomes arbitrarily small and hence harder to measure, but the time dilation effects become larger and hence much easier to measure. Confirming that a highly boosted particle does not cease to experience time entirely or experience time in reverse is typically much easier to do at extremely relativistic speeds than directly measuring distance measurements.

These calculations are not hard to do. I had problem sets in freshman physics that required that we make them. We had to take on faith the global average measurement of the decay rate of a muon at rest (for which the Particle Data Group provides a bibliography of the experimental results used to reach the result), and we had to take on faith that observed probability that of a particular energy decayed in a particular time period where we were given only the citation to the experiments finding that to be the case. But, with those empirically confirmable measurements in hand, the math checked out and reproduced the observed behavior.

Coming up with a theory that has a formula which exhibits this asymptotic behavior everywhere we can observe it that is exactly the same as special relativity, but which somehow allows a massive particle to reach light speed, is not easy.

In contrast, the speed of light pops out naturally even from the classical Maxwell's equations, the relationship can be deduced logically from other axioms, and we can even measure the speed of light indirectly from general relativity, for example, by using the E=mc^2 relationship to match the expected and observed energy output of a nuclear reaction, or of matter-antimatter annihilation (which also checks out to the limits of experimental accuracy). The fact that the value of "c" in general relativity and special relativity is robust over many different kinds of measurements suggests that the quantity "c" in those equations is an accurate conceptualization of the way that the world really works. Finding an alternative theory in which "c" holds over such a robust range of measurements is much harder than devising a theory that allows massive objects to travel at exactly "c" in just one kind of measurement (like the direct neutrino speed measurement recently conducted by MINOS).

Precise time measurements are also used to test gravitational time dilation. For example, scientists have put one atomic clock at the top floor of the National Institute of Standards building, where the gravitational field is slightly weaker, and another in the basement, where the gravitational field is slightly stronger, and observed precisely and in statistically significant amounts the amount of time dilation due to gravity as would be expected from the differences in the strength of the gravitational field caused by a ca. 50 foot difference in altitude.

Both experiments indirectly prove the formulas relating mass, gravitational field strength, and velocity of special relativity and general relativity respectively in a quantitative manner.

While we can't directly measure the difference between a light relativistic particle and a particle moving at exactly the speed of light with quite as high precision, we can confirm with high precision that the formulas of the theory hold in every circumstance we can measure it, and compare those results with any alternative proposed theory. Special relativity predicts that in the MINOS neutrino case that neutrino speed is less than c by about 1 part per 10^18. The experiment showed that the difference was less than 1 per per 10^6, which is consistent with that result. This may not, by itself, convince you that massive objects can never get all of the way to the speed of light. But, it should convince you that the linear Newtonian mechanics relationship between force and velocity does not hold true, which definitively displaces the most intuitive alternative.

Since general relativity and special relativity match with extreme precision in every circumstance we can measure to within the experimental margin of error, we presume that the theory will continue to hold in more extreme circumstances in the absence of any reason to doubt the result.

Also, because special relativity and general relativity (at least in so far as time dilation due to gravity and E=mc^2) show such precisely and consistent relationships across such a robust range of measurement types, even if we found an experimental case where this did not seem to hold true, we would be inclined to consider other explanations (e.g. that there might be a small number of tiny wormholes for short distances in a given volume, on average, in the topology of seemingly empty space, or that what we were measuring the speed of light in wasn't actually a vacuum) as opposed to trying to tweak special relativity and general relativity per se.

 

[SpiderET]

To give an example of how we experimentally confirm special relativity; special relativity predicts the time dilation expected of a short lived particle like a muon, as a function of its speed which is in turn a function of its kinetic energy. Muons accelerated with 100 GeV of energy each are going to have a half-life in the reference from of observers at rest in the particle accelerator of X which is much longer than the half-life of a muon not accelerated. The relationship between the energy we use to accelerate a muon and its observed half-life, corresponds closely to the expected value. If the muon were going at exactly the speed of light, however, we would expect the muon to never decay, which is not what we observe, even when we give the muon immense energy boosts. The asymptotic behavior of muon decay rates with respect to energy of acceleration is very powerful evidence that special relativity is true, and if special relativity is true, then massive objects can't actually reach the speed of light.

It turns out to be much easier to measure the energy of acceleration and the decay rates with minimal systemic error, than it is to measure speed itself, because at high energies the marginal increase in velocity from an increase in energy is so small. As energies get higher relative to particle mass, the difference between "c" and the particle's speed in your reference frame becomes arbitrarily small and hence harder to measure, but the time dilation effects become larger and hence much easier to measure. Confirming that a highly boosted particle does not cease to experience time entirely or experience time in reverse is typically much easier to do at extremely relativistic speeds than directly measuring distance measurements.

These calculations are not hard to do. I had problem sets in freshman physics that required that we make them. We had to take on faith the global average measurement of the decay rate of a muon at rest (for which the Particle Data Group provides a bibliography of the experimental results used to reach the result), and we had to take on faith that observed probability that of a particular energy decayed in a particular time period where we were given only the citation to the experiments finding that to be the case. But, with those empirically confirmable measurements in hand, the math checked out and reproduced the observed behavior.

Coming up with a theory that has a formula which exhibits this asymptotic behavior everywhere we can observe it that is exactly the same as special relativity, but which somehow allows a massive particle to reach light speed, is not easy.

In contrast, the speed of light pops out naturally even from the classical Maxwell's equations, the relationship can be deduced logically from other axioms, and we can even measure the speed of light indirectly from general relativity, for example, by using the E=mc^2 relationship to match the expected and observed energy output of a nuclear reaction, or of matter-antimatter annihilation (which also checks out to the limits of experimental accuracy). The fact that the value of "c" in general relativity and special relativity is robust over many different kinds of measurements suggests that the quantity "c" in those equations is an accurate conceptualization of the way that the world really works. Finding an alternative theory in which "c" holds over such a robust range of measurements is much harder than devising a theory that allows massive objects to travel at exactly "c" in just one kind of measurement (like the direct neutrino speed measurement recently conducted by MINOS).

Precise time measurements are also used to test gravitational time dilation. For example, scientists have put one atomic clock at the top floor of the National Institute of Standards building, where the gravitational field is slightly weaker, and another in the basement, where the gravitational field is slightly stronger, and observed precisely and in statistically significant amounts the amount of time dilation due to gravity as would be expected from the differences in the strength of the gravitational field caused by a ca. 50 foot difference in altitude.

Both experiments indirectly prove the formulas relating mass, gravitational field strength, and velocity of special relativity and general relativity respectively in a quantitative manner.

While we can't directly measure the difference between a light relativistic particle and a particle moving at exactly the speed of light with quite as high precision, we can confirm with high precision that the formulas of the theory hold in every circumstance we can measure it, and compare those results with any alternative proposed theory. Special relativity predicts that in the MINOS neutrino case that neutrino speed is less than c by about 1 part per 10^18. The experiment showed that the difference was less than 1 per per 10^6, which is consistent with that result. This may not, by itself, convince you that massive objects can never get all of the way to the speed of light. But, it should convince you that the linear Newtonian mechanics relationship between force and velocity does not hold true, which definitively displaces the most intuitive alternative.

Since general relativity and special relativity match with extreme precision in every circumstance we can measure to within the experimental margin of error, we presume that the theory will continue to hold in more extreme circumstances in the absence of any reason to doubt the result.

Also, because special relativity and general relativity (at least in so far as time dilation due to gravity and E=mc^2) show such precisely and consistent relationships across such a robust range of measurement types, even if we found an experimental case where this did not seem to hold true, we would be inclined to consider other explanations (e.g. that there might be a small number of tiny wormholes for short distances in a given volume, on average, in the topology of seemingly empty space, or that what we were measuring the speed of light in wasn't actually a vacuum) as opposed to trying to tweak special relativity and general relativity per se.

Thanks for good and quite extensive response.
Yes, you have a good point about the muons, it shows it from different angle. But when you look on it from different angle, I could do it too.
What if all particles have mass, including photon? Then there would be no infinite time dilation. Regarding theory, it seems to me that there would be only minor changes needed and these changes would be more about philosophical approach than about real changes in equotations. All experiments would be in line with the same equotations and E=mc2 would mean that matter is not 100% transferred to energy but to photons which would have very tiny invariant mass. Currently, there is very low probability that photon has mass and relevant experiments have pushed the limit to very low levels. Similar to measurements of approaching speed of light, we could say that it is reasonably confirmed that photon has no mass, but on the other hand, there is no absolute disproof of photon with mass.

And regarding speed of light popping out naturally from Maxwell equotations I would rather say that is is open question. Speed of light comes from experimentally measured permeability and permitivitty of vacuum and when we discard circular arguments, nobody really knows why is it so.
http://physics.stackexchange.com/qu...s-the-permittivity-and-permeability-of-vacuum

 

[ZapperZ]

Currently, there is very low probability that photon has mass and relevant experiments have pushed the limit to very low levels. Similar to measurements of approaching speed of light, we could say that it is reasonably confirmed that photon has no mass, but on the other hand, there is no absolute disproof of photon with mass.

I'm going to criticize you for taking this kind of an approach to your argument. If you are going by what can't be absolutely disproved (as if there is such a thing in science), then I'd say that there's no absolute disproof that photons can't collide and produce a unicorn.

If you start resorting to supporting your argument using what can't be disproved, rather than what is probable and realistic, then this will not be a rational discussion that will go anywhere. Resorting to such a thing will mean that you will start reaching for the bottom of the bottom of the barrel and every point you make will be nothing more than speculation.

Is this what you prefer to do?

Zz.

 

[bcrowell]

There was a very nice educational experiment done on this topic by Bertozzi back in the 1960s that was designed to be simple for students to understand. There was a paper and an accompanying video.

Bertozzi, "Speed and kinetic energy of relativistic electrons," Am. J. Phys. 32 (1964) 551, https://www.scribd.com/doc/258743358/Bertozzi-Speed-and-kinetic-energy-of-relativistic-electrons-Am-J-Phys-32-1964-551

video: https://www.youtube.com/watch?v=B0BOpiMQXQA

 

[ohwilleke]

What if all particles have mass, including photon? Then there would be no infinite time dilation. Regarding theory, it seems to me that there would be only minor changes needed and these changes would be more about philosophical approach than about real changes in equotations. All experiments would be in line with the same equotations and E=mc2 would mean that matter is not 100% transferred to energy but to photons which would have very tiny invariant mass. Currently, there is very low probability that photon has mass and relevant experiments have pushed the limit to very low levels. Similar to measurements of approaching speed of light, we could say that it is reasonably confirmed that photon has no mass, but on the other hand, there is no absolute disproof of photon with mass.

The question of whether a photon could have infinitessimal mass is a very different one than the question of whether a massive object could travel at a velocity c rather than almost c.

This would have almost no measureable effect on the velocity of a photon (by assumption), and almost no measureable effect on the gravitational interactions of a photon (since gravity couples to mass-energy, rather than only mass; one term of the stress-energy tensor would be infinitessimally smaller, and several other elements would be tiny but non-zero). There is a considerable literature regarding the quite similar issue in many respects of the possibility of a massive graviton.

The most stringent limitation on a massive photon, I would think, would be that there would be the absence of any evidence of an asymptotic relationship between the frequency (which is proportional to energy) and motion of a photon, over the entire range from very low frequency radio waves to X-rays. Given the extreme precision with which these have been measured, the bound on a rest mass for a photon that would be consistent with experimental data within error bars would be very tiny (much, much smaller, for example, than the meV mass scale of neutrino masses, for example).

Another set of experimental data that would tightly constrain this hypothesis is the array of astronomy data that has been marshaled to rebut the "tired light" hypothesis (Google it).

 

[Dale]

What if all particles have mass, including photon?

There is extensive literature on the consequences of massive photons. Please do not speculate on what you think the consequences might be.

Thread closed.