# Thoughts on Einstein’s Theories

I believe Einstein said,

1.There are four dimensions to space, the normal three plus time.
2. Speed of light cannot be obtained due to an object traveling at such speeds
gaining mass. The faster it goes, the more mass gained, until it reaches “infinite mass”.
3. Mass and Energy are pretty much the same thing in different states.
4. E=MC2, Or… you can got a whole lot of energy from a pretty small item.

Ok, based off of all of that.

To get to the speed of light you have to burn off mass as fast as your gaining it, perhaps by some kind of controlled chain reaction. Using the mass your burn off to propel yourself. (Perhaps also a means of pretty much limitless power. By creating something you can accelerate a particle in so it will gain mass that you could then “burn off” for power).

Now, it would seem odd that just moving creates mass. Unless it is due to energy created by moving through space/time, like friction from moving through air.

Of course if Time truly is a force that we can feel, then it would seem moving through at higher speeds does a couple things. There is resistance and there is energy/mass attached to or generated by whatever is moving through at high speeds. It would also stand to reason, some sort of wake would be created, much like a submarine moving through water would create. (I wonder if that would be somehow detectable).

Another thought on this. If anything reaches this point of “infinite mass” what happens if it weakens, or goes critical? Could the Big Bang have been the result of a near infinite mass particle going at light speed?

It makes sense that time actually slows down for someone going at such high speeds. If your falling from an airplane the air seems to be “rushing past you”, all due to mass and air resistance, etc…you even reach a “terminal velocity”. However if you went flying past someone floating in the air, their experience would be much different then the falling person. Therefore pushing your way through time and space, leaving who knows what kind of wake behind, (the source of deja vu?). Time, like water would be forced to move aside and around you. Again this suggests even more that the mass gained is as much resistance by Time then anything else. However we cannot rule out energy created by this resistance doesn’t attach itself to said speeding object, perhaps “charging” it somehow, truly increasing the mass of the object.

Or perhaps Time is the force that controls how fast electrons go around a neutron, the force that controls how fast things decay, etc. Pushing through it…the resistance created could force things like atomic clocks to slow down. Perhaps not truly effecting “Time”.

Time may truly be less of a means to which one would mark passing events, and more the very thing that ties everything together.

Now one of the issues is of course what happens if you can get to the speed of light? Say for instance you build a ship that you propel forward, as the ship gains speed, it gains mass, (Is it also gaining potential or kinetic energy?), and say you find away to actually turn that mass into more energy to continue propelling it forward? Surely that would be one impressive explosion. What effect would that have on the space/time continuum itself? Or would the resulting mass and energy discharge actually warp space around you?

Thoughts and replies appreciated.

Joe Carron

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This post would be better suited for the relativity forum.

nuke_c said:
I believe Einstein said,

1.There are four dimensions to space, the normal three plus time.
Saying "there are four dimensions to space" is inaccurate. The correct way to state this is there are four spacetime dimensions. When the three dimensions of space and the one dimension of time are unified as spacetime, relativity can be seen as rotations in spacetime geometry. Hermann Minkowski was the first to prove this using Einstein's special theory of relativity. Einstein himself originally disliked the idea of unified spacetime, but he quickly changed his mind when he began searching for a relativistic theory of gravity; his general theory of relativity is founded on four dimensional spacetime.

nuke_c said:
2. Speed of light cannot be obtained due to an object traveling at such speeds
gaining mass. The faster it goes, the more mass gained, until it reaches “infinite mass”.
This is one way of looking at it, but most agree it is not the best way. Everything in relativity can be explained without resorting to saying an object gains mass as it speeds up (if you define mass as something unrelated to speed). Mass can, however, be defined as something that is related to speed; this is called relativistic mass. Relativistic mass does increase with speed, but most people here prefer not to use the idea of relativistic mass because it isn't necessary and leads to confusion (such as in your case).

The easiest way to show that nothing can reach the speed of light is by using the relativistic addition of velocities equation:
$$v_{AC}=\frac{v_{AB}+v_{BC}}{1+\frac{v_{AB}v_{BC}}{c^2}}$$

As long as you fill in values for $v_{AB}$ and $v_{BC}$ which are less than $c$ (the speed of light), you always end up with a $v_{AC}$ which is also less than the speed of light. No matter how much you accelerate you can never surpass the speed of light. There are other, more complete, ways of proving this using the Lorentz transformations and relativistic energy equations, but this method seems easiest to understand without a lot more explanation.

Thank you for your input on this. I am uncertain I fully follow though, it seems that as speed increases you still have a force that works against you to achieve light speed.

If it is not mass gained, is it more like resistance of timespace, not so disimilar then wind on a running person?

wht u truly missed-out is the time-dilation factor @ relativistic speed...
the faster u travel thru space, the slower u travel thru time...
each event that u excperience will be subjected to time-dilation...
in otherwords, u wont be able to burn the last few drops of fuel to get passed the speed of light coz as u approach 'C,' time dilation will tend to infinity..
working with the tranformation equations will help u understand better...

Oh I follow! Thank you. I will give that some more thought. I will also check out the transformation equations.

Again I appreciate the input.

Ok, one more quick question. Why is it that light can go that speed. How does it avoid the time-dilation factor and such? Is it due to it's near zero mass? (Or is it zero mass?)

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nuke_c said:
Ok, one more quick question. Why is it that light can go that speed. How does it avoid the time-dilation factor and such? Is it due to it's near zero mass? (Or is it zero mass?)

Right. Any massless particle HAS to move at c in relativity. And it has no rest frame or proper time as a result, but it does have momentum and energy. The photon is strongly believed to be strictly massless; if it were not we would see light compression waves. Instead the light waves are strictly transverse.

When neutrinos were thought to be massless they were considered to move at c; now that they are known to have a tiny mass, they are understood to move at a little less than c, and to have rest frames and proper times. The case of neutrinos and photons is different. There is no strong physics like the absence of light compression waves favoring a massless neutrino; it was just that their mass was so small and observing neutrinos is so difficult that it was decades before the mass could be inferred.

Doesn't that just leave you with the question "what exactly is mass?"?

Fine, I can see that a consequence of not having mass implies travel at c, but how is that different from saying "rest mass is to a certain extent the measure of the extent to which a particle-wavelet does not travel at c"?

My understanding is that the only reason they are saying that neutinos don't travel at c is that they suspect they have mass, or have they actually been able to measure their speed? And how do they know that the neutrinos actually have mass? Is it meaningful to say they have mass, or could it be possible to say that "under certain circumstances neutrinos have mass-like properties"? (Especially if we have problems saying precisely what mass is.)

A lot of questions I know, sorry ...

Also...if I understand what you were saying correctly, if you were to use the gained mass as a source of power, say, by converting it into energy, you would lose acceleration from the lack of mass. And about the time-dilation...time would be going extremly slow, however, as time is relative, time would pass normally for the object as long as time was still moving, therefore it would not be a problem. Please correct me if I'm wrong :(. P.S. Do photons avoid the time dilation of travelling at c? I always thought that because they did, they were destroyed the instant in which they were created relative to them as time stands still for anything travelling at the speed of light. Hmmmm...

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neopolitan said:

Doesn't that just leave you with the question "what exactly is mass?"?

Fine, I can see that a consequence of not having mass implies travel at c, but how is that different from saying "rest mass is to a certain extent the measure of the extent to which a particle-wavelet does not travel at c"?

My understanding is that the only reason they are saying that neutinos don't travel at c is that they suspect they have mass, or have they actually been able to measure their speed? And how do they know that the neutrinos actually have mass? Is it meaningful to say they have mass, or could it be possible to say that "under certain circumstances neutrinos have mass-like properties"? (Especially if we have problems saying precisely what mass is.)

A lot of questions I know, sorry ...

Well mass in the standard model is a fraught issue, as I have posted before.

The case of the neutrinos is interesting. As you may know, there are three "flavors" or generations of neutrinos, associated with the electron, muon, and tauon respectively. Years ago the famous Homestake Mine neutrino "telescope" turned up that there were only abour a third as many neutrinos coming from the Sun as the solar physics should make. Physicsts noted that Homestake only looked at electron neutrinos, and it was suggested maybe the neutrinos could turn into each other on the way from the Sun. If Homestake was sampling an average steady state with equal counts in each of the three flavors, then it would only see a third of the total.

Later the Super Kamiokande neutrino obsertvatory in Japan confirmed the neutrino oscillation. But if the neutrinos were to engage in physical processes like oscillation during their trip from the Sun to the Earth, then they must have experienced proper time on that trip. A particle traveling at c experiences no proper time, it experiences being born at its source and immediately being absorbed at its target. So proper time for neutrinos implies they don't travel at c, and hence that they cannot be massless, so they have mass. Super Kamiokande has also measured the mass.

?llipse said:
This is one way of looking at it, but most agree it is not the best way.
Did someone do a survey that I was unaware of? In any case opinion means nothing when it comes to the best results (i.e. least errors). The way you're speaking of leads to more errors than I can count.

Pete

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From what I can tell looking around, they haven't actually measured a mass for neutrinos, or rather there are a few experiments extant and they all point to a negative mass-squared for a neutrino, which is rather odd. Most sites I've found use the word "ambiguous", so to claim the mass has been measured is maybe overstating the case.

Mathematically there are some Weyl equations which point to neutrinos having a mass of zero (http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:hep-ph/0009291 [Broken]), which if valid puts us in a position where neutrino mass must be zero and also can't be zero ... unless the interpretation of the oscillations is incorrect.

We cannot tell what state a neutrino takes until it interacts with something, so is it possible that the neutrino doesn't have a definite state until it interacts, and that some aspect of the interaction results in the neutrino taking a certain state or another? Observationally this would be the same as if the neutrinos changed state in transit (which as you point out implies real time and hence mass), but because the effect only manifests while the neutrino is actually being absorbed, then there is no need for assuming oscillations in transit, and hence no need to assume mass. Note that most of the experiments to determine neutrino mass-squared have sufficient error to incorporate a zero mass result (see here). This doesn't explain why neutrino mass-squared appears to be negative though.

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neopolitan said:

From what I can tell looking around, they haven't actually measured a mass for neutrinos, or rather there are a few experiments extant and they all point to a negative mass-squared for a neutrino, which is rather odd. Most sites I've found use the word "ambiguous", so to claim the mass has been measured is maybe overstating the case.

Any physical measurement has an expected error band, and the one for the neutrinos is fairly big; neutrinos are VERY hard to see! The mean of the measurements of m^2 are above zero but the error band, or at least the early ones, dips below zero. Some eager beavers jumped on that t o say that neutrinos might be tachyonic, but I'm pretty sure later observations didn't confirm this. Nevertheless the process of measuring the mass has begun and is an ongoing project with improving accuracy.

Mathematically there are some Weyl equations which point to neutrinos having a mass of zero (http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:hep-ph/0009291 [Broken]), which if valid puts us in a position where neutrino mass must be zero and also can't be zero ... unless the interpretation of the oscillations is incorrect.

The equations can't "prove" anything about nature. It's just a question of which odels to use. There are puzzles about neutrinos, like the fact that there are no observed right-handed neutrinos - and that constrains the models and is a hot topic right now, but there is no conflict like you believe.

We cannot tell what state a neutrino takes until it interacts with something, so is it possible that the neutrino doesn't have a definite state until it interacts, and that some aspect of the interaction results in the neutrino taking a certain state or another? Observationally this would be the same as if the neutrinos changed state in transit (which as you point out implies real time and hence mass), but because the effect only manifests while the neutrino is actually being absorbed, then there is no need for assuming oscillations in transit, and hence no need to assume mass. Note that most of the experiments to determine neutrino mass-squared have sufficient error to incorporate a zero mass result (see here). This doesn't explain why neutrino mass-squared appears to be negative though.

Your attempt to deny the neutrinos have attributes when not interacting (Copenhagen) still does not satisfy the condition. If there are X number of neutrinos produced in solar fusions, and allowing for the cross-section of the neutrino detector only X/3 interactions are found you still have a puzzle. Inded this was the original puzzle, because they were assuming zero-mass neutrinos and zero proper time in transit. I repeat the oscillation has been definitely observed and that requires greater than zero proper time, and that in turn implies greater than zero mass, from relativity. The measurements of mass are an addition, but this line of reasoning is firm.

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I'm not denying anything, and I'm not make pronouncements on anything, I'm asking. The whole neutrino mass thing seems odd, that is all.

hungrytrash said:
Also...if I understand what you were saying correctly, if you were to use the gained mass as a source of power, say, by converting it into energy, you would lose acceleration from the lack of mass. And about the time-dilation...time would be going extremly slow, however, as time is relative, time would pass normally for the object as long as time was still moving, therefore it would not be a problem. Please correct me if I'm wrong :(. P.S. Do photons avoid the time dilation of travelling at c? I always thought that because they did, they were destroyed the instant in which they were created relative to them as time stands still for anything travelling at the speed of light. Hmmmm...

My thoughts were based on the idea that it wasn't due to having mass at all that kept you from gaining lightspeed, it was the appearance of gaining mass that kept it from happening. ie...as you go faster your mass increased thus requiring more energy to continue to go faster. I had thought that if you could convert that additional mass into energy using it for propulsion you could keep the mass the same, relative to time and I believe speed. So you would try to keep your "at rest" state of mass the same, as your approached c. Again that was my question.

From what I believe is being said here, it is the fact you have any mass at all that keeps you from gaining c. I am sure there are some theories about creating some kind of field around your "ship" to make at seem as though you have zero mass..or bending space or what have you, but that I am sure is a discussion for another thread elsewhere.

Later the Super Kamiokande neutrino obsertvatory in Japan confirmed the neutrino oscillation. But if the neutrinos were to engage in physical processes like oscillation during their trip from the Sun to the Earth, then they must have experienced proper time on that trip. A particle traveling at c experiences no proper time, it experiences being born at its source and immediately being absorbed at its target. So proper time for neutrinos implies they don't travel at c, and hence that they cannot be massless, so they have mass. Super Kamiokande has also measured the mass.

Is it not possible for something that is massless to travel at less then c? Assuming a vaccuum.

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nuke_c said:
Is it not possible for something that is massless to travel at less then c? Assuming a vaccuum.
As has happened in other threads, there is some confusion over different meanings of "mass".

For those who don't know

• the invariant mass (or "rest mass", or "proper mass") of a particle excludes kinetic energy (remember mass implies energy)
• the relativistic mass of a particle includes kinetic energy
(Experienced readers might quibble with my definitions but I'm trying to keep it simple.)

Different contributors to this thread have used the word "mass" to refer to one or other of the above without specifying which. Talk of mass increase as you approach the speed of light implies relativistic mass. Talk of massless particles implies invariant mass.

To answer nuke_c's question: Something with zero invariant mass always travels at c (the speed of light in a vacuum).

The energy of a particle with invariant mass $m$ at speed $v$ is given by
$$E = \displaystyle{\frac{m c^2}{\sqrt{1-v^2/c^2}}}$$
If you put $v=c$ you get infinity (the mathematician's way of saying "impossible"). The only way to avoid infinity is to put $m=0$.

But if $m=0$ and $v<c$ you get zero energy (and zero momentum and zero mass of either type) -- in other words, nothing, it doesn't exist.

(In the special case where $m=0$ and $v=c$ the equation for $E$ fails and becomes $E = pc$ where $p$ is momentum.)

reilly