Some say that the reason you can't travel faster than light is that your mass will increase as your speed approaches light speed – so, regardless of how much energy your star drive can generate, you reach a point where no amount of energy can further accelerate your spacecraft because its mass is approaching infinite.

This line of thinking is at best an incomplete description of what’s really going on and is not a particularly effective way of explaining why you can’t move faster than light (even though you can’t). However, the story does offer some useful insight into why mass is equivalent to energy, in accordance with the relationship e=mc^{2}.

Firstly, here’s why the story isn’t complete. Although someone back on Earth might see your spacecraft’s mass increase as you move near light speed – you certainly aren’t going notice your spacecraft’s, or your own, mass change at all. Within your spacecraft, you would still be able to climb stairs, jump rope – and if you had a set of bathroom scales along for the ride you would still weigh just the same as you did back on Earth (assuming your ship is equipped with the latest in artificial gravity technology that mimics conditions on Earth’s surface).

The change perceived by an Earth observer is just relativistic mass. If you hit the brakes and returned to a more conventional velocity, all the relativistic mass would go away and an Earth observer would just see you retaining with same proper (or rest) mass that the spacecraft and you had before you left Earth.

The Earth observer would be more correct to consider your situation in terms of momentum energy, which is a product of your mass and your speed. So as you pump more energy in to your star drive system, someone on Earth really sees your momentum increase – but interprets it as a mass increase, since your speed doesn’t seem to increase much at all once it is up around 99% of the speed of light. Then when you slow down again, although you might seem to be losing mass you are really offloading energy – perhaps by converting your kinetic energy of motion into heat (assuming your spacecraft is equipped with the latest in relativistic braking technology).

From the perspective of the Earth-based observer, you can formulate that the relativistic mass gain observed when travelling near light speed is the sum of the spacecraft’s rest mass/energy plus the kinetic energy of its motion – all divided by c^{2}. From that you can (stepping around some moderately complex math) derive that e=mc^{2}. This is a useful finding, but it has little to do with why the spacecraft’s speed cannot exceed light speed.

The phenomenon of relativistic mass follows a similar, though inverse, asymptotic relationship to your speed. So as you approach light speed, your relativistic time approaches zero (clocks slow), your relativistic spatial dimensions approach zero (lengths contract) – and your relativistic mass grows towards infinite.

But as we’ve covered already, on the spacecraft you do not experience your spacecraft gaining mass (nor does it seem to shrink or have its clocks slow down). So you must interpret your increase in momentum energy as a genuine speed increase – at least with respect to a new understanding you have developed about speed.

When you approach light speed and still keep pumping more energy into your drive system, what you find is that you keep reaching your destination faster – not so much because you are moving faster, but because the time you estimated it would take you to cross the distance from point A to Point B becomes perceivably much less, indeed the distance between point A to Point B also becomes perceivably much less. So you never break light speed because the distance over time parameters of your speed keep changing in a way that ensures that you can’t.

In any case, consideration of relativistic mass is probably the best way to derive the relationship e=mc2 since the relativistic mass is a direct result of the kinetic energy of motion. The relationship does not easily fall out of consideration of (say) a nuclear explosion – since much of the energy of the blast derives from the release of the binding energy which holds a heavy atom together. A nuclear blast is more about energy transformation than about matter converting to energy, although at a system level it still represents genuine mass to energy conversion.

Similarly you might consider that your cup of coffee is more massive when it’s hot – and gets measurably less massive when it cools down. Matter, in terms of protons, neutrons, electrons …and coffee, is largely conserved throughout this process. But, for a while, the heat energy really does add to the mass of the system – although since it’s a mass of m=e/c^{2}, it is a very tiny amount of mass.

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Light speed

## antialias_physorg

Which is pretty much summed up by the author description in the original article:

## Ddoodle

I think clearing the stuff up is much more important than just showing another new looking discovery which has actually been discovered many years before but maybe in a slightly different version.

And i think physorg now totally recognized this.

## Ddoodle

## Mayday

I love this stuff.

## alfredh

## Isaacsname

Of course, I'm just repeating what I learned watching Susskind's lectures on youtube, to the my best recollection. I think it's lecture 6 of the cosmology series he explains this.

## Royale

## richgibula

## PermanentMarker

## RealScience

No, you don't pay it back. Even when slowing down you are still 'saving time' because you are still going faster than when at rest.

richgibula:

A megaton is a million tonnes (metric tons) of TNT, where the energy of a gram of TNT is defined as 4184 Joules (one kCal). A tonne a million grams, so that is 4.2x10^15 Joules.

C is 3x10^8 meters/sec, so C^2 is 9x10^18, which is ~2000 times bigger. So a 1 megaton H-bomb convert about 1/2 gram of matter to energy.

## Isaacsname

http://www.youtub...e=relmfu

## Vendicar_Decarian

worst ever

## jsa09

The problem a lay person has boils down to not appreciating a speed limit.

The best explanation would avoid any reference to a speed limit and fix the perceived problem from an alternate view point.

Look at velocity from the point of view of the traveler. Question: How long would it take me to fly to the nearest star which is 4 light years away?

Answer: depends how fast you go. Given a very powerful engine you could be there in a year, a month, a day, an hour or whatever.

Question: But what about the speed limit?

Answer: There is no speed limit you just have to speed up the universe to get there sooner and that uses a lot of fuel.

## jsa09

Maybe all accelleration applies to yourself pushing the universe. The faster you want to travel the harder you push.

## Rohitasch

## richgibula

Thank you for your response, but I have an additional question. You said:

"A megaton ...convert about 1/2 gram of matter to energy."

But the author said: "A nuclear blast is more about energy transformation than about matter converting to energy"

Is there a calculation for how much energy release each source contributes to the whole?

## RealScience

In a chemical explosion, it is the atoms' electrons that change configuration to release energy.

In a nuclear explosion, it is the protons and neutrons that are rearranged to release energy.

In either case the energy released is reflected by the reaction products (once cooled and at rest) having less mass than the starting material had. The change is very small - even in a hydrogen bomb the energy released is less than 1% of the mass of the nuclei involved.

## Callippo

http://www.pitt.e...oof.html

We can understand it easily with using of water surface model of space-time. The energy introduced makes it undulating and elongated like the deformed carpet. This deformation slows down another particles of matter, which are traveling across undulating place, so it behaves like are of more dense matter. The E=mc^2 is therefore the relation between deformation of space-time and energy introduced into this deform and it's valid only for 4D space-time. At the 3D space-time it would correspond E=mc and so on. The introduction of extradimensions therefore changes the E=mc^2 formula and general relativity should account into it, when describing the hyperdimensional effects, like the dark matter.

## antialias_physorg

The energy released in a nuclear blast (if I remember that lecture by Feinman correctly) is a rearrangement (transformation) of neutrons/protons from larger nuclei to smaller ones. The energy released is electrostatic energy. the number of protons and neutrons (and electrons) after a nuclear blast are the same as before. The energy content of those products is, however, less - since they are now rearranged into more stable configurations (and some neutrons flying off on their own)

So really we're not dealing with a 'nuclear' (force) bomb but with an 'electrostatic' bomb. The nuclear forces actually get a bit larger - they are a negative contribution to the energy output.

## RealScience

But most of the energy of a hydrogen bomb comes from fusion of hydrogen isotopes, typically deuterium and tritium.

Thus most of the energy of a 1-megaton bomb is from very small nuclei fusion into fairly small nuclei. In this the energy released comes from the strong nuclear force, with the electrostatic potential increasing.

## antialias_physorg

## eljo

If your mass increases with speed, does the energy contained in that mass also increase? And if so does the energy content of the propulsion fuel you carry with you also increase? Meaning that the energy you carry to propel your ship is always in proportion to energy needed to propel the mass of the ship? Does this mean that accelerating to light speeds is just a question of accelerating long enough without it becoming more difficult to accelerate at all, does it become easier (e.g. you need less fuel to accelarate even more the quicker you go)?

Just asking.

## Callippo

http://aetherwave...ent.html

It means, the mass of objects in motion increases with the mass of surrounding vacuum, which is dragged and shaken by their motion, not by mass of objects itself. The area of dense vacuum slows down the light spreading with respect to observer, so it participates to the relativistic length contraction too.

## Callippo

In dense aether model your relativistic speed is followed with area of dense vacuum, which increases your mass with respect to other observers. But when some observer is moving with relativistic speed in the same direction, like you, then you're both surrounded with the same area of dense vacuum and you cannot detect any gain in mass, after then. Because you're both surrounded with vacuum of the same relative density.

## MorituriMax

Other than that, not sure why it is here.

About the length contraction thing, I wonder if as your relativisitc mass goes up you actually do something to the fabric of space-time that makes it harder for you to keep accelerating closer and closer to C.

jsa09, please don't do us any more "favors" in trying to make it easier to understand.

## dchris

## Callippo

Basically because of geometry of energy wave spreading with limited speed. As usually in dense aether theory, the water surface analogy explains it well: http://www.aether...rnik.gif

The length contraction is the necessary consequence of the constant speed of light postulate of special relativity.

http://aetherwave...peed.gif

## wpdwpd

What you are referring to is the state of displacement of the aether.

Aether has mass. Aether is physically displaced by matter.

The faster an object moves through the aether the more aether the object displaces the greater the relativistic mass of the object.

## rawa1

Therefore the inertial wave equation formalism can be applied to the vacuum as well. For example, when we undulate elastic material of final mass density, this material will increase its density for all waves which are passing trough the undulating place accordingly.

## wpdwpd

The elastic material is the aether. Aether has mass.

## wpdwpd

The elastic material is the aether. Aether has mass.

'From Analogue Models to Gravitating Vacuum'

"The aether of the 21-st century is the quantum vacuum, which is a new form of matter. This is the real substance"

"Einstein's 'First Paper'"

"The velocity of a wave is proportional to the square root of the elastic forces which cause [its] propagation, and inversely proportional to the mass of the aether moved by these forces."

## Callippo

## wpdwpd

Pressure exerted by displaced aether toward matter is gravity.

A moving particle has an associated aether displacement wave. In a double slit experiment the particle enters and exits a single slit and it is the associated aether displacement wave which enters and exits both. As the wave exits the slits it creates wave interference. As the particle exits a single slit the direction it travels is altered by the wave interference. This is the wave piloting the particle of pilot-wave theory. Detecting the particle turns the associated aether displacement wave into chop, there is no wave interference, and the direction the particle travels is not altered.

Curved spacetime is displaced aether.

## Callippo

## wpdwpd

A boat's bow wave is its water displacement wave. A moving boat physically displaces the water into the form of a wave.

A moving particle physically displaces the aether into the form of a wave.

## MarkyMark

## rawa1

I've no connection to wpdwpd. It just illustrates, the aether model leads to the reproducible conclusions.

## wpdwpd

It's aether displacement wave. In a double slit experiment the particle enters and exits a single slit and it is the associated aether displacement wave which enters and exits both.

## rawa1

## wpdwpd

"The walkers wave is similar to the surface wave of a raindrop falling on a puddle"

A raindrop falling on a puddle creates a ripple because the raindrop displaces the water in the puddle.

The physical wave of de Broglie wave mechanics is an aether displacement wave.