# Question on Special Relativity.

• BathingGrape
In summary: I don't know for sure, but doesn't Hawking radiation defy the speed...Theoretically, yes. If something has a high enough speed, then it would escape the radiation. However, we don't actually know of anything that has that high of a speed. Theoretically, yes. If something has a high enough speed, then it would escape the radiation. However, we don't actually know of anything that has that high of a speed.
BathingGrape
Hello everyone, I'm new here: I just wanted to ask one question that was bothering me. You see, I've just started reading about modern physics; for example, quantum physics and general relativity - and their possible unification through superstring theory (yes, I'm reading "The Elegant Universe"!). Anyway, my question is this:

First off, you need to be familiar with the theoretical "light clock", where a photon travels between two mirrors, and its used to keep time. The experiment showed special relativity, by demonstrating that if observed in movement, the proton will take longer to hit each mirror, and therefore time will move more slowly. So my question is simple and probably easily answerable: what would happen if the light clock was moving at light speed?

Here is a picture of the "light clock" (it seems they have actually made one).

http://www.physorg.com/newman/gfx/news/LightClock.gif

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Even if it was possible to make mirrors which could move at the speed of light, there'd be no way to aim a beam of light at them so that the light would bounce back and forth between them. Can you see why?

So my question is simple and probably easily answerable: what would happen if the light clock was moving at light speed?
Useless speculation. The clock cannot achieve light speed in any reference frame.

I understand you could not make a light clock move at light speed, it was hypothetical. So does that just mean that even hypothetically, its foolish to consider things moving at light speed?

Things with mass yes. Of course a photon always propagates at c.

BathingGrape said:
I understand you could not make a light clock move at light speed, it was hypothetical. So does that just mean that even hypothetically, its foolish to consider things moving at light speed?

Yes, actually. The rules of Relativity say that nothing with mass can travel the speed of light. If you hypothosis that it can, you are assuming that Relativity doesn't hold, and if Relativity doesn't hold, what rules do you use to predict what will happen? You can't invalidate the light speed rule without invalidating the whole theory.

in the limit of the speed of the clock approaching c, the clock will appear to tick slower and slower. the time for each tick approaches infinity as the speed of the clock approaches c.

I don't see anything wrong, in principle, with a massless mirror (of course, there's nothing like that that actually exists, but I don't see how it conflicts with the general principles of relativity), but like I said, you wouldn't be able to make a light clock out of it.

Thanks a lot for all the responses, they made a lot of sense.

Take the (sqrt of 1 - v^2/c^2) part of the E=mc^2 equation.

Of course that is on the bottom of the fraction, therefore if you have a velocity that equals the speed of light, you get the square root of 1 -1, which is 0, and it is undefined, you cannot divide by zero.

Therefore, you will not go the speed of light.

Riogho said:
Take the (sqrt of 1 - v^2/c^2) part of the E=mc^2 equation.

Of course that is on the bottom of the fraction, therefore if you have a velocity that equals the speed of light, you get the square root of 1 -1, which is 0, and it is undefined, you cannot divide by zero.

Therefore, you will not go the speed of light.

Is this really the only reason we think we cannot achieve Light Speed, or Greater than Light Speed?

Michamus said:
Is this really the only reason we think we cannot achieve Light Speed, or Greater than Light Speed?

No it appears that the fundamental speed limit of the Universe is indeed c. However were we to detect something achieving equal to or faster than c with mass - or for that matter without mass achieving something in excess of c - then it would prove the theory wrong; so far we haven't. So we take the equations to demonstrate the effect of acceleration on anything with mass, equations which happen to also match experimental outcomes. It's a mathematical model, but it wouldn't exist if it's posits didn't equate with the reality of experiment.

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Schrodinger's Dog said:
No it appears that the fundamental speed limit of the Universe is indeed c. However were we to detect something achieving equal to or faster than c with mass - or for that matter without mass achieving something in excess of c - then it would prove the theory wrong; so far we haven't. So we take the equations to demonstrate the effect of acceleration on anything with mass, equations which happen to also match experimental outcomes. It's a mathematical model, but it wouldn't exist if it's posits didn't equate with the reality of experiment.

I don't know for sure, but doesn't Hawking radiation defy the speed of light? Since the Uncertainty Principle in quantum mechanics allows for some particles to just appear outside of a black hole, causing its evaporation. Is this true, or are my sources false? (My sources were a transcript of one of Hawking's lectures.) Or did I just read the lecture wrong?

BathingGrape said:
I don't know for sure, but doesn't Hawking radiation defy the speed of light?
I'm not quite sure why you'd think this. There's nothing that says a particle "emitted" via Hawking radiation is traveling faster than the speed of light. Unless, of course, you're thinking of the situation as a particle actually being emitted from behind the black hole event horizon, which is not what Hawking radiation is (because, of course, no particle can escape from behind an event horizon). If this is what you're thinking, then let us know and I'm sure someone will provide an explanation.

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Well, I've looked through what lectures of Hawking that I could find, and I can't seem to find it. Perhaps I read it incorrectly. I swear what I read was along the lines of "due to the Uncertainty Principle, some particles can appear outside of a black hole, and thus travel faster than light; this is Hawking Radiation". Now like I said, I am most likely wrong. But I have one more question: you mentioned that a particle can be emitted from behind a black hole's event horizon. Since nothing, not even light, can escape a black hole, how can any particle be emitted from a black hole? Wouldn't this require traveling faster than light speed? Anyway, thanks for all the answers; like I said, I'm new to studying physics, so any correction only helps me.

BathingGrape said:
you mentioned that a particle can be emitted from behind a black hole's event horizon.

Nope, I mentioned this thinking that you may have a misconception that this happens. Particles certainly do not "come out" of the event horizon. Hawking radiation arises when a particle-antiparticle pair are formed from the vacuum, just outside the event horizon of a black hole. This happens all the time, everywhere in space, but the particles annihilate each other within a very short amount of time, and so we see no consequence of this. However, if such a pair is produced on the edge of a black hole, then one particle can fall into the hole, leaving nothing for the other one to annihilate with. Thus, this particle is free, and the energy of the universe has increased (this is the Hawking radiation). Thus, to compensate, the particle that has fallen into the black hole reduces the energy of the black hole.

Ok, that makes sense. Thanks a lot! So since I read you wrong and its not Hawking radiation, what is the name for this phenomenon?

BathingGrape said:
Ok, that makes sense. Thanks a lot! So since I read you wrong and its not Hawking radiation, what is the name for this phenomenon?

I've edited my first post, since it seems to read badly. No particle can escape from behind a black hole's event horizon.

Ah thank you for editing that. I figured that was the source of confusion, but I didn't want to point it out and sound arrogant and all, especially since I'm new. Thanks though, I finally have a definitive answer.

## 1. What is special relativity?

Special relativity is a theory developed by Albert Einstein that describes the relationships between space and time. It explains how objects and events appear differently to observers moving at different speeds and how these differences can be calculated.

## 2. How does special relativity differ from general relativity?

Special relativity deals with the relationship between space and time in the absence of gravity, while general relativity incorporates the effects of gravity into these relationships. Special relativity is also limited to objects moving at constant speeds, while general relativity applies to both constant and accelerating speeds.

## 3. What is the concept of time dilation in special relativity?

Time dilation refers to the phenomenon in which time appears to pass slower for a moving object than for a stationary one. This effect is due to the fact that the speed of light is constant and the passage of time is relative to an observer's frame of reference.

## 4. Can special relativity be proven?

Special relativity has been extensively tested and has been proven to accurately describe the behavior of objects and events at high speeds. Many experiments, such as the famous Michelson-Morley experiment, have consistently confirmed the predictions of special relativity.

## 5. How does special relativity impact our everyday lives?

Special relativity has had a significant impact on our understanding of the universe and has led to advancements in technology, such as GPS systems. It also plays a crucial role in many other areas of physics, including quantum mechanics and cosmology.

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