# Dumb questions about E=mc2 and other things...

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#### mrmux

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I read somewhere that a square mile of sunlight, on Earth, exerts a 'pressure' of about 3lbs.<br /><br />How do we know photons are truly massless? And why doesn't plugging that zero into E=mc2 mean that photons therefore have zero energy?

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#### Saiph

##### Guest
because photon energy is derived by a different means, and E=hf where H is plancks constant and F is frequency, C is well "c".<br /><br />E=mc^2 is really just a truncated version of the full equation: E^2 = m^2c^4 + p^2c^2<br /><br />It's often truncated because you wish to deal only with stationary matter. If it isn't moving p=0 and that second term drops out. Then you take a nice square root, and you end up with the correct E=mc^2.<br /><br />So, we if photons have no mass, but they have energy...the equation just above shows they also have momentum. To show this, put in m=0. In this case the <i>first</i> term drops out, leaving only the second term, showing that you can also define the energy of a photon by it's momentum (or vice versa). Photons have energy, and momentum, but do not require mass.<br /><br />As for proof the photon is massless...quantum electrodynamics (a very accurate and succesful theory) basically hits a brick wall and falls apart if photons do. Experiments also set a very firm upper limit to a photons mass, and that limit is very, very, very small (basically "no" mass detected).<br /><br />Here's a couple of links:<br /><br />http://math.ucr.edu/home/baez/physics/Relativity/SR/light_mass.html<br /><br />http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html<br /><br /> <div class="Discussion_UserSignature"> <p align="center"><font color="#c0c0c0"><br /></font></p><p align="center"><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">----</font></em></font><font color="#666699">SaiphMOD@gmail.com </font><font color="#999999"><em><font size="1">-------------------</font></em></font></p><p><font color="#999999"><em><font size="1">"This is my Timey Wimey Detector.  Goes "bing" when there's stuff.  It also fries eggs at 30 paces, wether you want it to or not actually.  I've learned to stay away from hens: It's not pretty when they blow" -- </font></em></font><font size="1" color="#999999">The Tenth Doctor, "Blink"</font></p> </div>

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#### mrmux

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You the man, Saiph. <br /><br />I accept space is bendy. Clocks don't really work, fine. Now you tell me momentum can exist without mass.<br /><br />Goddammit, I know nothing. I'll learn though.

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#### Saiph

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hey, just think, people accuse physicists of being to stiff when it comes to <i>new</i> ideas like antigravity and ESP.<br /><br />Most of them don't know what's bandied about everyday, and generally accepted/used.<br /><br />For example, a gentleman came up to me and started talking about UFO's and why they go after cows and drunks, then talked about a cover up.<br /><br />I then asked if he would believe that physicists acknowledge, and use regularly, that the faster one travels the shorter the total distance they have to travel. Not as in they cover the distance faster, but that the actual distance is less.<br /><br />He wouldn't swallow it, not even when I said that was Special Relativity.<br /><br />Go figure. <div class="Discussion_UserSignature"> <p align="center"><font color="#c0c0c0"><br /></font></p><p align="center"><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">----</font></em></font><font color="#666699">SaiphMOD@gmail.com </font><font color="#999999"><em><font size="1">-------------------</font></em></font></p><p><font color="#999999"><em><font size="1">"This is my Timey Wimey Detector.  Goes "bing" when there's stuff.  It also fries eggs at 30 paces, wether you want it to or not actually.  I've learned to stay away from hens: It's not pretty when they blow" -- </font></em></font><font size="1" color="#999999">The Tenth Doctor, "Blink"</font></p> </div>

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#### mrmux

##### Guest
Oh you just love this, don't you? You should be a teacher, saiph! You know full well I have to ask you about that now.<br /><br />The actual distance is less? Is that as measured 'on board'? Not just because of the time experienced?<br /><br />Holy crap.<br />

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#### Saiph

##### Guest
Well, you have to remember, the time measured "on board" seems no different. They measure a second as a second.<br /><br />However, the outside frame can be said to be "moving" in special relativity. As such the outside frame experiences time dilation (it's clocks move slow relative to the ship), which is the foundation of the classic twin "paradox".<br /><br />The outside frame <i>also</i> experiences length contraction in the direction of travel, thus the ship actually measures a shorter distance to the destination.<br /><br />It makes some sense if you think about how things must work out in the end. Earth knows the ship is moving (as the ship accelerates and decelerates, breaking "reciprocity") as earth doesn't feel any change in motion, but the ship does.<br /><br />So the earth, and the ship, when they compare clocks after the trip will both agree that the ships clocks are those that are slow.<br /><br />So, a trip at .866c to alpha centauri takes 4.6 years. The ships clock (and earth's reading of the ships clock) says it took 2.3. So, how'd the ship go 4 light years in a percieved time of 2.3 years? Thats faster than light!<br /><br />If you factor in the length contraction, the ship actually observes the distance to alpha centauri to be only 2 light years.<br /><br />The ship, before stopping, measured as shorter distance, and expects to arrive in 2.3 years (the time dilated duration). Earth sees it as 4 ly, and expects a 4.6 ly trip, but knows the ships clock is going to run slow.<br /><br />The only reason this comes out to an "absolute" answer of who was slower, etc. is because one of the groups accelerated.<br /><br />And as for becoming a teacher...I intend to. I've been a tutor/teachers assistant during my undergraduate career, and I'm now taking on the role as a graduate student. <div class="Discussion_UserSignature"> <p align="center"><font color="#c0c0c0"><br /></font></p><p align="center"><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">----</font></em></font><font color="#666699">SaiphMOD@gmail.com </font><font color="#999999"><em><font size="1">-------------------</font></em></font></p><p><font color="#999999"><em><font size="1">"This is my Timey Wimey Detector.  Goes "bing" when there's stuff.  It also fries eggs at 30 paces, wether you want it to or not actually.  I've learned to stay away from hens: It's not pretty when they blow" -- </font></em></font><font size="1" color="#999999">The Tenth Doctor, "Blink"</font></p> </div>

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#### mrmux

##### Guest
Saiph, you are a gentleman as well as a scholar. <br /><br />I was correct then; the answer really is, 'holy crap'. How the hell did anyone work this out? You wouldn't imagine it in a million years, no matter what the experiments said.<br /><br />I'm truly baffled - and I hate being baffled. I understand what you are saying, but I... still don't. How do physicists sleep at night anyway?<br /><br />It will obviously take much more learning than I thought to escape my mental Flatland. Good!<br /><br />Re: time dilation/approaching lightspeed, etc. Does that apply to light itself? From a photon's perspective, does everything happen simultaneously?<br /><br />Please say no...

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#### Saiph

##### Guest
well...sorry to say, but yes. Time is stationary for a photon. It's emission, traveling deflections, refractions, and absorption are...done at the same time as far as the photon is concerned.<br /><br /> <div class="Discussion_UserSignature"> <p align="center"><font color="#c0c0c0"><br /></font></p><p align="center"><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">----</font></em></font><font color="#666699">SaiphMOD@gmail.com </font><font color="#999999"><em><font size="1">-------------------</font></em></font></p><p><font color="#999999"><em><font size="1">"This is my Timey Wimey Detector.  Goes "bing" when there's stuff.  It also fries eggs at 30 paces, wether you want it to or not actually.  I've learned to stay away from hens: It's not pretty when they blow" -- </font></em></font><font size="1" color="#999999">The Tenth Doctor, "Blink"</font></p> </div>

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#### abhinavkumar_iitr05

##### Guest
Hello MrMux<br /><br />Its absolutely true that photons exert pressure on the bodies on which they r falling.I don't know about the exact magnitude of the force exerted by them when they fall on the earth<br /><br />Answering your question<br />How do we know photons are truly massless?<br />what I would like to say is that while saying photons r massless we actually mean their rest mass & not the dynamic one.Both rest & dynamic mass r related by Einstein's Special Theory of Relativity.Now thus the momentum associated with the moving photon is given by "planck const./wavelength".We have to consider this to explain the reason why not the mass becomes infinite when moving at a speed of light.<br /><br />The answer to ur next part is that this formula is actually the relation between the mass & amount of corresponding energy.Now here the photon is not converted into energy but the appearance of energy takes place due to the motion of the photons which equals to the product of planck constant & frequency of the photons.

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##### Guest
Perhaps em waves are a third state & applying mass or energy rules to them is wrong which is why we get such peculiar answers in order to fit.<br />Devising experiments to prove the status quo do just that & we need to think beyond it maybe.

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#### Saiph

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well...the thing is sairad...applying those rules produces the right answers. And very accurately.<br /><br />So the right answer, will incorporate these rules, or something very like them. <div class="Discussion_UserSignature"> <p align="center"><font color="#c0c0c0"><br /></font></p><p align="center"><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">----</font></em></font><font color="#666699">SaiphMOD@gmail.com </font><font color="#999999"><em><font size="1">-------------------</font></em></font></p><p><font color="#999999"><em><font size="1">"This is my Timey Wimey Detector.  Goes "bing" when there's stuff.  It also fries eggs at 30 paces, wether you want it to or not actually.  I've learned to stay away from hens: It's not pretty when they blow" -- </font></em></font><font size="1" color="#999999">The Tenth Doctor, "Blink"</font></p> </div>

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##### Guest
I once took one of those tests where you're given just enough information to find the solution. You know Jim likes carrots, Fred lives in a red house etc.<br />I got the right answer for an entirely wrong reason but could explain how, which could not be faulted, although it relied on me realising the mind of the writer & using other information shared by our minds.<br />Right answer wrong reason as it didn't rely on embedded information or did it as I was mind-reading?<br />So yes, the present <i>may</i> contain the rules but have we realised them or just using mind-reading?<br />

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#### Saiph

##### Guest
ahh, but I'm sure you also used many of the same logic structures to get to your answer, you followed the same general rules.<br /><br />There are also often many ways to get the same answer. In QM we have wave mechanics (schroedinger) and matrix based math (Heisenberg). Two entirely different approaches, one using wave equations and differential equations, the other using linear algebra, matrices, and a handful of special rules (limitations really). But they give the exact same answers...and can actually be proven to be equivelant systems in other aspects. <div class="Discussion_UserSignature"> <p align="center"><font color="#c0c0c0"><br /></font></p><p align="center"><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">----</font></em></font><font color="#666699">SaiphMOD@gmail.com </font><font color="#999999"><em><font size="1">-------------------</font></em></font></p><p><font color="#999999"><em><font size="1">"This is my Timey Wimey Detector.  Goes "bing" when there's stuff.  It also fries eggs at 30 paces, wether you want it to or not actually.  I've learned to stay away from hens: It's not pretty when they blow" -- </font></em></font><font size="1" color="#999999">The Tenth Doctor, "Blink"</font></p> </div>

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