# E=MC2: does this prevent a Mass from achieving Light Speed?

1. Jan 11, 2004

### timejim

I say NO. If energy can be converted to Mass and Mass can be converted to Energy, then, being a layman, what would prevent any object from being propelled to the speed of light without, as I have heard, requiring all the energy in the Universe to do so?

2. Jan 11, 2004

### mathman

The problem of getting to light speed comes from the Lorentz transformation on the mass. Mass increases without limit as an object gets close to light speed, so almost all the energy applied to such objects goes into increased mass and very little into increased speed.

3. Jan 11, 2004

### timejim

I know, this is what I have heard, but sometimes, irregardless of Scientific Theorey and calculation, when an actual experiment or endeavor occurs, strange, unexpected things have happened that baffles the experts. I have a funny feeling someday in the future something completely unexpected will occur.

4. Jan 11, 2004

### fffbone

Give us an example.

In the field of physics? I doubt it.

5. Jan 11, 2004

Staff Emeritus
Around the world are hundreds of particle acclerators, capable of driving particles up to near the speed of light in order to smash them into targets and thus maybe create new particles or at least new examples of decays to study.

In the course of this they have to calculate the particle appoaching the target, its time (i.e lifetime if its a short-lived particle), its dimensions, its momentum and its energy. All of these things vary according to the Lorentz transformations of relativity based on the relative speed between the particle and the target.

In ALL OF THESE EXPERIMENTS which run into the hundreds of thousands over many decades, the Lorentz transformations are validated. Accurately and in detail. There is no better validated theory on earth, not even Newton's or Maxwell's, than special relativity.

6. Jan 11, 2004

### David

There is a big question about this right now, because of the “superluminal” galaxies that appear to be moving away from the earth at high speeds such as 3c and 4c.

So, if you accept that, then there is a way out of the dilemma, if we say that the light speed is a “limiting speed” inside a strong gravitational field, under the terms of the Lorentz theory of relativity and his theory of electrodynamics. But, if the distant galaxies are not moving through strong gravitational fields, then there appears to be no speed limit on them. This tends to fit in to GR theory too.

According to the 1895 and 1904 Lorentz relativity theory, the “fields” put up a physical resistance to the rapid motion of atoms, and it was he, not Einstein, who calculated the limiting speed, with his Lorentz Transformation equation. Lorentz’s 1904 paper was titled, “Electromagnetic Phenomena in a System Moving with any Velocity Less than that of Light.”

The earth-based particle accelerators are resting inside a strong gravitational field. The distant and rapidly galaxies evidently are not.

7. Jan 11, 2004

### David

It was actually Newton, not Einstein, who first said that light energy could be converted into mass and mass converted into light energy. See Newton's "Optics", 1704.

Einstein got most of his basic ideas from Newton and Lorentz. In fact, it was Newton, in “Optics”, who first said a light ray would bend as it passed astronomical bodies like the sun and moon.

It was Lorentz, in his 1904 paper, who developed the idea of mass increase due to speed, time dilation, and length contraction. In fact, he had length contraction in his 1895 paper.

8. Jan 11, 2004

### Staff: Mentor

Thats self-contradictory: If mass is converted to energy, then it isn't mass anymore. And energy (electromagnetic radiation) travels at the speed of light.

9. Jan 12, 2004

### Tron3k

You should use the correct equation:

$$E = \frac{m_0 c^2}{\sqrt{1 - v^2/c^2}}$$

So as speed approaches c, E approaches infinity.

10. Jan 12, 2004

### Arcon

Then what you're saying is that the predictions of relativity are wrong. While it may be true that relativity will someday predict something which is then proved wrong by experiment it does not mean that if I apply a constant force on a particle that it reaches or surpases the speed of light. A constant force means that work is always being done on the particle and the kinetic energy is always increasin and therefore the speed is always increasing. But just because the speed is always increasing it doesn't follow that the speed will equal that of light someday. It just keeps getting closer to the speed of light.

This is the case in particle accelerators today. We can get protons and electrons to almost the speed of light but never equal to the speed of light

11. Jan 12, 2004

### Arcon

Re: Re: E=MC2: does this prevent a Mass from achieving Light Speed?

That's not quite correct. What Newton said was
That speaks to a relation between light and matter. Not energy and mass. It doesn't say that mass increases when a body recieves light and it does not even say that light has energy. I don't believe anyone knew that light had energy in those days.

And I believe it was Soldner and Cavendish who first proved that light is bent by the sun. However they were off by a factor of two.

Please post a quote from "optics" where he said that astronomical bodies bent light. Thanks.

12. Jan 12, 2004

### Nereid

Staff Emeritus
I think you may be confusing two different things - jets from AGNs (quasars, Seyferts, etc) and maybe 'microquasars', and 'high-z' galaxies (galaxies with redshifts >1). In either case, the observations are quite consistent with Relativity.

To clarify, would you mind giving a source? Then we can discuss these apparent speeds.

13. Jan 12, 2004

### Arcon

Note the term "apparent" in that? The observations can be described using special relativity. The analysis is consistent with the observations and the analysis does not contain anything which is moving faster than the speed of light.

In fact there was an article published in the American Journal of Physics which uses quasars to help teach special relativity

The use of quasars in teaching introductory special relativity, Denise C. Gabuzda, Am. J. Phys. 55, 214 (1987)

In fact Taylor and Wheeler have a homework problem in their text Spacetime Physics 2n2 Ed. on page 90-90 which explains all of this.

In essence what is happening is that a piece of stellar material is moving at relativistic speeds but less than c. Think of the material as emitting flashes of light at an interval $$\Dt_{flash}$$ in a direction $$\theta$$ off from straight line motion. Let the distance between the locations where the flashes were emitted be $$\Delta x_{flash}$$. Then the time interval between at which the flashes arrive at the observer's location is

$$\Delta t_{flash} = \Delta t(1 - v cos \theta)$$

the ratio

$$v_{flash} = \frac {\Delta x_{flash}}{\Delta t_{flash}} = \frac {v sin \theta}{1 - v cos \theta}$$

is the speed that they're refering to when they speak of this so-called superluminal motion. This quantity can be greater than c even when v is less than c. The maximum value of this is

$$v_{flash, max} = \frac {v }{\sqrt{1 - v^{2}}}$$

which is obvioulsy greater than c even when v < c.

14. Jan 12, 2004

### David

Re: Re: Re: E=MC2: does this prevent a Mass from achieving Light Speed?

“Do not bodies act upon light at a distance, and by their actions bend its rays; and is not this action strongest at the least distance?

If refraction be performed by attraction of the rays, the sines of incidence must be to the sines of refraction in a given proportion, as we shewed in our principles of philosophy: And this rule is true by experience.” Newton, 1704

“Doth not this aether in passing out of water, glass, crystal, and other compact and dense bodies into empty spaces, grow denser and denser by degrees, and by that means refract the rays of light not in a point, but by bending them gradually in curve lines? And doth not the gradual condensation of this medium extend to some distance from the bodies, and thereby cause the inflexions of the rays of light, which passes by the edges of dense bodies, at some distance from the bodies?

And though this increase of density may at great distances be exceedingly slow, yet if the elastick force of this medium be exceedingly great, it may suffice to impel bodies from the denser parts of the medium towards the rarer, with all that power which we call gravity?” Newton, 1704

“By equation 4 a ray of light passing along by a heavenly body suffers a deflection to the side of the diminishing gravitational potential, that is, on the side directed toward the heavenly body..” Einstein, 1911

“Are not gross bodies and light convertible into one another...?

The changing of bodies into light and light into bodies, is very conformable to the course of nature, which seems delighted with the Transmutations.” Newton, 1704

“If a body gives off the energy L in the form of radiation, its mass diminishes by L/c^2.” Einstein, 1905

15. Jan 12, 2004

### David

Yes, see the Davis-Lineweaver paper and discussions about it on the internet.

You can also find this info in some papers about superluminal galaxies that some cosmologists are actually moving away from the earth at greater than c.

See this:

“One such concept of general relativity is that we should not think of galaxies rushing away from us through a fixed space, we should think of galaxies more or less standing still in their local space but that space itself is expanding. This is a difficult concept but it can be described mathematically. In this concept, light leaving a distant galaxy is traveling at velocity c toward us in that local space but since space itself is expanding and that local space is moving away from us, the velocity of a light packet toward us (defined in a certain way) is less than c until the packet gets to our local space and the velocity can even be negative for some early portion of the time light travels to us.”

http://216.239.57.104/search?q=cach...+comoving+space+light+velocity&hl=en&ie=UTF-8

What this means is that if a galaxy is moving away from the earth at a speed greater than “c”, then the light that galaxy emits is aimed at the earth but it is moving away from the earth, relative to the earth, as it is emitted at the galaxy, but it is moving at “c” relative to that galaxy. Later during the light travel, the photons speed up relative to the earth and we finally receive it traveling at “c” relative to the earth.

This subject is not discussed very much yet, since it seems to violate Einstein’s “constancy” postulate of the 1905 theory. However, he altered that original concept with his 1911 GR theory, and that allows light move slow or even backwards, under certain circumstances, relative to the earth.

Einstein didn’t talk about this “backwards” light or a negative speed of light relative to the earth, because he died before any of the 1c, 2c, or 3c galaxies were discovered.

Last edited by a moderator: Apr 20, 2017
16. Jan 13, 2004

### Kurdt

Staff Emeritus
tron is right the mathematical model for this means that as the speed approaches the speed of light the denominator becomes zero and thus the value tends to infinity.

If the model is successful at explaining every high energy phenomena there is to date then there is no reason to doubt the prediction that this makes. Although one must maintain the premise that a theory can never be proved so one time in the future it may be disproved. As for the present we accept the limitations of the model as being correct as all evidence points to that notion

17. Jan 13, 2004

### DW

Even an ideal photon rocket couldn't do it. Lets consider the scenario that you are suggesting where a ship burns down its own mass as fuel and in the ideal case emmits a beam of light for its propulsion. If the instantaneous port frame exaust speed is $$v_{ex}$$ and the initial mass of ship and fuel carried is $$m_i$$ and the final mass is $$m$$ then a change in rapidity $$\theta$$ will be given by
$$\Delta \theta = \frac{v_{ex}}{c}ln(\frac{m_i}{m})$$.
The final speed can be calculated from the rapidity by
$$v = ctanh\theta$$
For large amounts of fuel burnt off even in the ideal photon rocket case where $$v_{ex} = c$$ the hyperbolic tangent of the rapidity approaches 1 so that the speed still only approaches c. Interestingly this is even the case if the exaust were itself tachyonic with $$v_{ex} > c$$.

Last edited: Jan 13, 2004