# Gravitational Effect of Electromagnetic Radiation

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1. Feb 28, 2015

### Jon Mel

Hello PPer's,

I have been considering the effect to which electromagnetic radiation emitted from stars might play in the gravitational coalescence of galaxies. Surrounding every galaxy there must be a halo of electromagnetic radiation streaming outwards at the speed of light which diminishes according to the inverse square rule. From the billions of stars converting their mass into pure energy the gravitational effect of this halo can be estimated. This energy is otherwise largely invisible because it does not have the chance to interact with much as it moves away from the galaxy and into open space. In fact these photons exist as a quantum probability wave which will collapse only when they interact with other galaxies billions of years away. Yet they must exert a real gravitational effect as I will demonstrate with a rough calculation here:

Assuming our Sun to be an average star which will burn for 10 billion years and taking the Milky Way as being 100,000 light years across we can calculate that there is approximately, 1/(10^10 / 10^5) = 1/100,000 solar mass of electromagnetic radiation distributed in a 100,000 light year halo surrounding our galaxy just from our Sun.

Assuming the Milky Way to contain 100 billion stars of which the Sun is average then we have, 10^11 x 10^(-5) = 10^6, or 1 million solar masses of energy in this 100,00 light year halo.

Of course these assumptions take our Sun as losing all of its mass to photons which we know to be untrue, our Sun will lose much of its mass in solar winds when it is a red giant and will hold on to a lot of its mass later as an inert white dwarf. However larger stars burn quicker and more fully convert their mass into photons, leaving behind only supernovae remnants. These stars will therefore have a greater percentage of their total mass as electromagnetic radiation within the 100,000 light year halo at any one time, for example a 50 solar mass O-type star may have a life span of just 10 million years so that 1% of its mass, or 0.5 solar masses, could be having a gravitational effect from within the halo.

Of course the gravitational influence of this electromagnetic radiation would not stop at the 100,000 light year mark, it would only become more diffuse according to the inverse square rule with distance, so that at 200,000 light years it would have 1/4 of the gravitational effect on stars within, or outlying our Milky Way.

Would this gravitational effect explain, or partly contribute to an explanation, for dark matter?

2. Feb 28, 2015

### Orodruin

Staff Emeritus
Your computations (a) highly overestimates the amount of energy that can possibly be converted to photons in a star (iron has the largest binding energy per nucleus at about 8 MeV, compared to the proton mass of almost 1 GeV, the effect is less than one percent at most) (b) assumes an inverse square law for gravitation when considering relativistic particles, (c) I am probably missing something else, it is late here.

The answer to your question is simply "no". Also be aware that Physics Forums does not allow personal theories and this thread is already on the very border.

3. Feb 28, 2015

### Staff: Mentor

Power output of the Sun: 4x1026 watts = 4x1026 joules/second x 60 seconds x 60 minutes x 24 hours x 365.25 days x 10 billion years = 1.26x1044 joules.

1.26x1044 joules / 300 million2 (c2)= 1.4x1027 kg radiated away over the course of 10 billion years.

1.4x1027 kg / 1.99×1030 kg (1 solar mass) = 7.05x10-4 solar masses, or 0.000705 solar masses, radiated away over 10 billion years.

Hope my math is right.

4. Feb 28, 2015

### Jon Mel

Ok thanks guys, that knocks that idea on the head!

I'd still be interested to know if photons, being at the relativistic velocities they are, can indeed exert a gravitational effect even if it is infinitesimally small. If true, then surely this would negate the possibility of combining quantum mechanics with general relativity since the photon would be in a probability state whilst still interacting with the space-time field. Could the space-time field therefore drain energy from the photon whilst it is travelling long distances thereby causing a redshift effect?

5. Feb 28, 2015

### Staff: Mentor

Sure. They have energy and therefore will alter the stress-energy tensor, which is where gravitation comes from.