Expert: Jayendra Upadhye - 8/4/2008

Question
QUESTION: The orbit of the earth does not change around the sun and the rate of light the sun emits stay the same. But the rate of time on earth slows to 1/2 the current rate of time. The question is how much more light does the earth receive per unit of original time.

ANSWER: Hi,
Your question is really really strange to say the least.
Time cannot change rate "locally", for earth only, as you say, it has to change for the whole system! Else, the earth will slow down in orbit and crash into the sun!!

But converting your question a bit, i rephrase it thus:
"If time were to slow down for the solar system, how much light would the earth get per unit of original time"?

Well the answer is "the same"!! :)

Because, light is a wave. As time slows, it will also take more time to reach earth. So say if earth recieves x number of quanta per hour, now too it will recieve the same number! As it will take those quanta more time to reach by the factor by which time has slowed down!

View the universe as a continuum of snaphots of a photon stream and sun as source, and planets as recievers. Now speed up the rate of sucession of frames or slow them down, the number of quanta recieved will NOT vary, ONLY TIME (which is your frame rate) will vary!

To put it another way, it like running a movie frame by frame or at normal speed...the STORY (historical information content) remains the same!!

hope you get my point.

Please do rate the answer if you find it interesting.
regards
Jayen



---------- FOLLOW-UP ----------

QUESTION: I know this is more of a metaphysical question than a pure scientific question, but thank you for responding anyway. It seems to me with only the earth's local time twice as slow, would not the speed of light coming from the sun be measured as twice as fast. That would imply the photons from the sun would be detected at twice the rate, making the sun as twice as bright. Also the distance to the sun would be measured as 1/2 as far. Through geometrical effects, the 1/2 shorter distance would increase the number of photons hitting the earth by 4. Thus the total effect would be that the number of photons / s measured would increase by 8. Given these constraints would not that be correct?

Answer
Hi,
May be.
(thanks for your rating though).
The thing is, a lot more thought may have to be given to it.

But what shall we gain by doing such a thing?
one chief difficulty is since velocity is distance/time, if time rate is halved, velocity will "double"! C which is velocity of light, cannot be violated without serious errors.
So, light will have to get reddened as C = freq*wavelength and frequency will double, resulting in halved wavelength in order to keep C constant.

This is just the beginning of our difficulties.

But let the matter rest, i feel you must work this out by yourself.
regards
Jayen