A couple questions about relativity and space-time

[eldowan]

So, after reading a good bit of this thread, I had a couple of tangentially related questions that I was hoping someone could answer for me.

When objects move through space-time, is it like a submarine moving through water, where the surrounding environment is pushed out of the way to make room for a moving body? Or maybe is it more like a whiffle ball moving through water, where the object moves through the water, and the water (mostly) stays put?
Am I way off base?
Also, I limitedly understand that mass/energy are convertable. E=mc^2 and all that.
In the referenced thread, i forget the exact post, it is mentioned that photons are massless, and can therefore travel at the speed of light. I understand that as velocity increases, so too does mass, and that any massive object cannot accelerate to the speed of light, as the energy required approaces infinity as the velocity approaches c.

Where I get lost is how a photon can have energy and have no mass. I did a little reading and it just went all greek->latin->italian on me. Anyone care to explain?
Thanks,

[Terr]

@eldowan

Also, I limitedly understand that mass/energy are convertable. E=mc^2 and all that.
In the referenced thread, i forget the exact post, it is mentioned that photons are massless, and can therefore travel at the speed of light. I understand that as velocity increases, so too does mass, and that any massive object cannot accelerate to the speed of light, as the energy required approaces infinity as the velocity approaches c.

Where I get lost is how a photon can have energy and have no mass. I did a little reading and it just went all greek->latin->italian on me. Anyone care to explain?

The “E=mc^2” is shorthand, really. The equation is really “E^2=MR^2C^4+p^2c^2” where MR is “rest mass” and p is momentum.

If you look at that equation, and substitute 0 for “rest mass” of a photon, you will get

E=pc (where p is photon’s momentum).

[eldowan]

@Terr

The “E=mc^2” is shorthand, really. The equation is really “E^2=MR^2C^4+p^2c^2” where MR is “rest mass” and p is momentum.

If you look at that equation, and substitute 0 for “rest mass” of a photon, you will get

E=pc (where p is photon’s momentum).

Yes, I read that elsewhere before. But I don’t understand what it means.

So does this imply that when a photon is moving that mass is created for it? Since once acceleration begins, MR != 0.

[eldowan]

@eldowan

So does this imply that when a photon is moving that mass is created for it? Since once acceleration begins, MR != 0.

In thinking about this on the drive home, I realized that MR = 0 in all conditions, as MR, per the equation, is resting mass.

I still don’t get it any better, however.

[Terr]

@eldowan

Yes, I read that elsewhere before. But I don’t understand what it means.

So does this imply that when a photon is moving that mass is created for it? Since once acceleration begins, MR != 0.

MR (rest mass) of a photon is 0. There really is no “acceleration” for a photon - it cannot move at speed less than c.

You can think of it as if photon has no rest mass but has a “relativistic mass” - Mr=E/c^2. The more energetic the photon, the more “massive” it is.

[leahcim]

@eldowan

When objects move through space-time, is it like a submarine moving through water, where the surrounding environment is pushed out of the way to make room for a moving body? Or maybe is it more like a whiffle ball moving through water, where the object moves through the water, and the water (mostly) stays put?
Am I way off base?

Much more like the whiffle ball that the submarine. The idea that space-time is weird comes from relativity. The idea that space-time is fantastically squishy and we can shove it around willy-nilly comes from Star Trek.

Also, I limitedly understand that mass/energy are convertable. E=mc^2 and all that.
In the referenced thread, i forget the exact post, it is mentioned that photons are massless, and can therefore travel at the speed of light. I understand that as velocity increases, so too does mass, and that any massive object cannot accelerate to the speed of light, as the energy required approaces infinity as the velocity approaches c.

Where I get lost is how a photon can have energy and have no mass. I did a little reading and it just went all greek->latin->italian on me. Anyone care to explain?

I find it easier to think of energy and momentum as the fundamental quantities and mass as the derived quantity. Like all particles have energy, all particles have momentum, just intrinsically, and if the quantity E[sup]2[/sup]/c[sup]4[/sup]-p[sup]2[/sup]/c[sup]2[/sup] happens to be non-zero, then it has mass. For electrons the quantity is non-zero, for photons it just happens not to be.

[eldowan]

@leahcim

Much more like the whiffle ball that the submarine. The idea that space-time is weird comes from relativity. The idea that space-time is fantastically squishy and we can shove it around willy-nilly comes from Star Trek.

Thanks, I thought as much.

@leahcim

I find it easier to think of energy and momentum as the fundamental quantities and mass as the derived quantity. Like all particles have energy, all particles have momentum, just intrinsically, and if the quantity E[sup]2[/sup]/c[sup]4[/sup]-p[sup]2[/sup]/c[sup]2[/sup] happens to be non-zero, then it has mass. For electrons the quantity is non-zero, for photons it just happens not to be.

Interesting explanation, mass being consequential and not fundamental. Again, thanks.